UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED
MANAGEMENT INVESTMENT COMPANIES

ITEM 1. REPORT TO SHAREHOLDERS

Table of Contents

January 31, 2016 | Annual Report 1

Letter from the President

Dear Shareholder:

¡  AllianzGI NFJ Dividend, Interest & Premium Strategy Fund returned -11.08% on NAV and -18.68% on market price.

During the 12 month period ended January 31, 2016, the Russell 3000 Index, a broad measure of US stock market performance, declined 2.48%; the Russell 1000 Value Index, a measure of large-cap value-style stocks, fell 5.00%; and the Russell 1000 Growth Index, a measure of growth style stocks, gained 1.32%. Convertible securities, as reflected by the BofA Merrill Lynch All Convertibles Index, returned -8.26%.

Turning to the US economy, gross domestic product (“GDP”), the value of goods and services produced in the country, the broadest measure of economic activity and the principal indicator of economic performance, grew at an annual pace of 0.6% during the first quarter of 2015. US economic activity then improved, as the US Commerce Department reported that GDP expanded at a 3.9% annual pace during the second quarter of 2015. However, economic growth then slowed, as GDP grew at an annual pace of 2.0% during the third quarter of 2015. The US economic activity decelerated further, as the Commerce Department’s initial estimate showed that GDP – released after the reporting period had ended – grew at an annual pace of 0.7% for the fourth quarter of 2015.

After a prolonged period of accommodative monetary policy, the US Federal Reserve (the “Fed”) raised interest rates for the first time in nearly a decade at its December 2015 meeting. The US central bank boosted the target federal funds rate from a range between 0% and 0.25% to a range between 0.25% and 0.50%. In its official statement following its meeting in December the Fed said, “The stance of monetary policy remains accommodative after this increase, thereby supporting further improvement in labor market conditions and a return to 2 percent inflation.The [Federal Open Market] Committee expects that economic conditions will evolve in a manner that will warrant only gradual increases in the federal funds rate; the federal funds rate is likely to

2 Annual Report | January 31, 2016

We continue to advocate holding on to risk assets relative to bonds over the long run. However, there are several headwinds at this juncture, including continued Fed rate hikes, unfavorable valuations in some asset classes, low earnings growth, liquidity concerns and political risks. Against this backdrop, we believe we are in a low return environment. In this environment, we will attempt to be flexible and active to put our shareholders in a position to benefit from volatility at an asset-class level. As always, our investment teams will also use in-depth research and focus on quality and sustainability, to help them navigate the markets.

For specific information on the Funds and their performance, please review the following pages. If you have any questions regarding the information provided, we encourage you to contact your financial advisor or call the Funds’ shareholder servicing agent at (800) 254-5197. In addition, a wide range of information and resources is available on our website, us.allianzgi.com/closedendfunds.

Together with Allianz Global Investors Fund Management LLC, the Funds’ investment manager, and NFJ Investment Group LLC and Allianz Global Investors U.S. LLC, the Funds’ sub-advisers, we thank you for investing with us.

We remain dedicated to serving your investment needs.

Julian Sluyters

President & Chief Executive Officer

January 31, 2016 | Annual Report 3

Fund Insights

AllianzGI Diversified Income & Convertible Fund/AllianzGI Equity & Convertible Income Fund/AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited)

AllianzGI Diversified Income & Convertible Fund

For the period of from inception on May 27, 2015 through January 31, 2016 as provided by Doug Forsyth, CFA, Portfolio Manager.

For the period since inception through January 31, 2016, the AllianzGI Diversified Income & Convertible Fund (the “Fund”) returned -16.40% on NAV and -30.12% on market price.

During the period from the Fund’s inception through January 31, 2016, the Russell 1000 Growth Index, a measure of growth style stocks, returned -5.69%; High Yield securities, as reflected by the BofA Merrill Lynch High Yield Master II Index, returned -9.75%; and convertible securities, as reflected by the BofA Merrill Lynch All Convertibles Index, returned -14.40%.

Market Environment

Several factors influenced the equity, convertible and high-yield markets during the period – most notably oil prices, technical pressure and negative sentiment, the Fed’s activity, earnings, the dollar and global economic data.

The decline in the price of energy and other commodities had a significant impact on fundamental and operating statistics of the issuers within those industries, but had an even greater impact on investor sentiment.

The decline in oil prices was a drag on all three asset classes, but the high yield market was the most impacted.

Broker-dealer and bank regulations continued to weigh on the market. Broker-dealer and bank market-making – or the lack thereof, caused by government regulations and the desire to reduce risk exposure – has made for inefficient transfer pricing. This market-smoothing mechanism was an important component of high yield and some convertible bond price discovery. Consequently, small trades in many cases created an inappropriate impact on prices.

The Fed was slow to act in 2015. Finally, in December, the Fed funds rate was increased by 25 basis points. This level remains extremely accommodative, and while directionally different, it was still aligned with global monetary policy decision makers, who remained largely accommodative.

One more tangible aspect of a relatively better US economy and a tightening Fed was the continued strength of the US dollar. The strong dollar did not help earnings trends of multinationals or aid in exports. It also coincided with the decline in many commodity prices.

The Fed tightened in the fourth quarter after the US economy grew in 2015 and amid expectations that the economy could achieve sustainable growth in 2016. Economic

4 Annual Report | January 31, 2016

Fund Insights

AllianzGI Diversified Income & Convertible Fund/AllianzGI Equity & Convertible Income Fund/AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited) (continued)

conditions in the US continued to provide evidence that defaults will remain subdued. Unemployment fell to 5.0%, a low not seen for more than seven years – beneath the long-run average of 5.8%. Additionally, consumer spending expanded, housing values increased and automobile sales reached a record high.

The Chicago Board Options Exchange Volatility Index (VIX) increased concurrent with equity market volatility. The VIX ended the reporting period at 20.20 after starting at 13.27.

Portfolio Specifics

The Fund provided consistent income – over the reporting period.

In the equity sleeve, stock picking was strongest in the information technology, energy, and health care sectors. Conversely, security selection in the consumer staples and financials sectors hampered performance.

In the convertibles sleeve, energy, consumer discretionary and industrials exposure helped relative performance. Issue selection was positive in the consumer discretionary and industrials sectors, and an underweight in energy was beneficial. In contrast, financials, utilities and transportation hampered relative performance. Issue selection was negative in all three of those sectors. An underweight in financials and utilities also detracted.

In the high-yield sleeve, industries that helped relative performance in the period included energy, metals/mining ex steel, and telecom-wireline. Having no exposure to metals/mining ex steel had a positive impact. An underweight and issue selection in both energy and telecom-wireline were areas of strength. In contrast, banking, utilities, and chemicals detracted from relative performance. An underweight in banking had a negative impact. Issue selection in utilities and chemicals were areas of weakness.

Regarding the options strategy, many of the covered call option positions expired below strike and the portfolio was able to retain the set premiums.

AllianzGI Equity & Convertible Income Fund

For the period of February 1, 2015 through January 31, 2016 as provided by Doug Forsyth, CFA, Portfolio Manager.

For the twelve-month period ended January 31, 2016, the AllianzGI Equity & Convertible Income Fund (the “Fund”) returned -3.60% on NAV and -8.01% on market price.

During the reporting period, the Russell 1000 Growth Index, a measure of growth style stocks, advanced 1.32%; and convertible securities, as reflected by the BofA Merrill Lynch All Convertibles Index, returned -8.26%.

January 31, 2016 | Annual Report 5

Fund Insights

AllianzGI Diversified Income & Convertible Fund/AllianzGI Equity & Convertible Income Fund/AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited) (continued)

Market Environment

Several factors influenced the equity and convertible markets during the period – most notably oil prices, technical pressure and negative sentiment, the Fed’s activity, earnings, the dollar and global economic data.

The decline in the price of energy and other commodities had a significant impact on fundamental and operating statistics of the issuers within those industries, but had an even greater impact on investor sentiment. The decline in oil prices was a drag on both asset classes.

Broker-dealer and bank regulations continued to weigh on the market. Broker-dealer and bank market-making – or the lack thereof, caused by government regulations and the desire to reduce risk exposure – has made for inefficient transfer pricing. This market-smoothing mechanism was a component of some convertible bond price discovery.

The Fed was slow to act in 2015. Finally, in December, the Fed funds rate was increased by 25 basis points. This level remains extremely accommodative, and while directionally different, it was still aligned with global monetary policy decision makers, who remained largely accommodative.

One more tangible aspect of a relatively better US economy and a tightening Fed was the continued strength of the US dollar. The strong dollar did not help earnings trends of multinationals or aid in exports. It also coincided with the decline in many commodity prices.

The Fed tightened in the fourth quarter after the US economy grew in 2015 and amid expectations that the economy could achieve sustainable growth in 2016. Economic conditions in the US continued to provide evidence that defaults will remain subdued. Unemployment fell to a more than seven-year low of 5.0% – beneath the long-run average of 5.8%. Additionally, consumer spending expanded, housing values increased and automobile sales reached a record high.

The VIX increased concurrent with equity market volatility. The VIX ended the reporting period at 20.20 after starting at 19.43.

Portfolio Specifics

The Fund provided consistent income over the reporting period.

In the equity sleeve, stock picking was strongest in the energy, information technology, and industrials sectors followed by company specific outperformance in other sectors. Conversely, security selection in the consumer staples and financials sectors weighed on relative performance.

In the convertibles sleeve, the fund benefited from exposure in the financials, consumer discretionary and consumer staples sectors. Issue selection was positive in both financials

6 Annual Report | January 31, 2016

Fund Insights

AllianzGI Diversified Income & Convertible Fund/AllianzGI Equity & Convertible Income Fund/AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited) (continued)

and consumer discretionary. An overweight in consumer staples contributed to performance. In contrast, technology, materials and industrials exposure hindered relative performance, all of which exhibited negative issue selection.

Regarding the options strategy, many of the covered call option positions expired below strike and the portfolio was able to retain the set premiums.

AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

For the period of February 1, 2015 through January 31, 2016 as provided by Krysta Hill, Product Specialist Associate.

For the twelve month period ended January 31, 2016, the AllianzGI NFJ Dividend, Interest & Premium Strategy Fund (the “Fund”) returned -11.08% on NAV and -18.68% on market price.

During the reporting period, the Russell 1000 Value Index, a measure of large-cap value style stocks, fell 5.00%; and convertibles securities, as reflected by the BofA Merrill Lynch All Convertibles Index, returned -8.26%

AllianzGI NFJ Dividend, Interest & Premium Strategy Fund announced dividend changes in October of 2015. The decision to decrease the Fund’s quarterly distribution from 45 to 30 cents per share took into account many factors, including, but not limited to, the overall market environment and the Fund’s current and projected level of earnings, as well as the portion of the Fund’s distributions represented by return of capital historically and based on future projections taking into account the reduced distribution rate.

Market Environment

US equities dropped into negative territory during the reporting period ended January 31, 2016 as markets climbed down from record-high levels during the first quarter of 2015 and ended the longest unbroken string of advances in more than twenty-five years. Investors grappled with the prospect of rate hikes at the Fed, the possibility that Greece might crash out of the euro zone and the potential for a deepening economic slowdown in China. Some of those threats were realized in the third quarter, which was marked by two key events: China’s August 11 currency devaluation and the September 17 US Federal Open Market Committee (“FOMC”) decision not to raise interest rates. While it probably wasn’t the intent of China’s policymakers, the 1.9% renminbi devaluation – the largest since 1994 – was interpreted, in part, as an attempt to counter slowing domestic demand by propping up exports. This sense of uncertainty was reinforced by the FOMC. Led by Fed Chair Janet Yellen, on December 16, the US central bank raised borrowing costs by 25 basis points to a new target range of 0.25% – 0.50%. The

January 31, 2016 | Annual Report 7

Fund Insights

AllianzGI Diversified Income & Convertible Fund/AllianzGI Equity & Convertible Income Fund/AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited) (continued)

decision brought to a close an unprecedented era of near-zero rates in the US.

Large capitalization and grow-oriented stocks led performance results over the reporting period as investors preferred larger capitalization and more liquid securities with higher growth prospects. Among the Russell style indices, the Top 200 Growth (4.5%) and Top 200 (0.6%) posted the best total returns, while the Microcap Growth, Microcap, 2000 Growth and 2000 Value indices fell 10% or more during the trailing twelve month period, ended January 31, 2016. Within the Russell 1000 Value index, telecom services and health care equities delivered the strongest performance results, with gains of 9.4% and 2.4%, respectively. Conversely, energy (-21.7%) and materials (-20.6%) were the poorest-performing sectors as falling oil prices negatively impacted equities across the domestic and international markets.

Several factors influenced the convertible market in the reporting period, including falling oil prices, economic data, increased market volatility and the Fed outlook.

One of the most influential factors impacting the convertible market was the drop in oil prices. Energy captured the attention of investors in the second half of the reporting period. While the energy sector represented only about 5% of the convertible universe, the decline in energy prices was a significant drag on the market. The fall in oil prices, along with continued weakness in natural gas prices, had a significant impact on the fundamental and operating statistics of energy-related issuers.

Another factor that influenced convertible markets was the ongoing trend in economic indicators. Throughout the reporting period, both current and expected statistics generally pointed to a US economy that is slowly grinding higher. While some of the data were mixed, many were positive, including employment and the ISM Manufacturing Index. These trends help confirm the prospects for the continued low default rate for convertible bonds.

Volatility appears to be a constant reminder of the changes in market dynamics. Pressure on banks and market makers, both regulatory and by their own design, to reduce inventory risk has increased the impact of buying and selling interest on pricing. For managers, this added complexity to trading resulting in more pressure on the market. Mutual fund flow data, news releases, external forces and equity volatility have all created more day-to-day volatility than typically seen historically, which can be unsettling for investors. However, absent a material change in the credit environment, this volatility also creates tremendous opportunity for investors.

As credit spreads widened during the reporting period, the majority of bond-like or yield-oriented convertible issues declined. While energy and commodity issues were

8 Annual Report | January 31, 2016

Fund Insights

AllianzGI Diversified Income & Convertible Fund/AllianzGI Equity & Convertible Income Fund/AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited) (continued)

responsible for a bulk of the decline, many small-cap convertible issues outside of commodities faced significant selling pressure. In many cases, the selling pressure on non-commodity issues was unwarranted based on fundamental change. Where fundamental changes did occur, the price reactions were extraordinary.

New convertible issuance brought the 2015 total to $39.3 billion. This compares with roughly $40.7 billion in maturities and redemptions.

Portfolio Specifics

In the equity sleeve, negative stock selection detracted from relative returns during the reporting period and sector allocation also detracted, albeit to a lesser degree. Selection was strong across the energy and telecom services sectors. However, that positive impact was overwhelmed by poor selection in the industrials, information technology and health care sectors. Overweight positions in the energy and materials sectors, as well as an underweight in utilities, dampened performance over the reporting period. Conversely, an overweight in telecom services aided relative results.

In the convertibles sleeve, sector allocations that helped relative performance in the period included consumer discretionary, industrials and consumer staples. In the consumer discretionary sector, an overweight and positive security selection were beneficial. The primary contributor in the industrials sector was issue selection. In the consumer staples sector, an overweight was a source of strength. In contrast, energy, healthcare and materials exposure weighed on relative returns. All of the three aforementioned sectors exhibited weaker issue-specific performance. In addition, an overweight in the energy sector and an underweight in the healthcare sector detracted.

In the equity option sleeve, calls written on the S&P 500 (used to add to exposure in multiple sectors such as healthcare, industrials, and materials) aided the relative returns in the period as we retained the majority of the premium on these options. Despite the overall negative broad market performance throughout the period, instances of strong equity performances in financials (from March through June and then again from September through November) and energy (from March through May) resulted in us not retaining any of our net option premium on those sectors for the period.

January 31, 2016 | Annual Report 9

Performance & Statistics

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (unaudited)

(1) Past performance is no guarantee of future results. Total return is calculated by determining the percentage change in NAV or market price (as applicable) in the specified period. The calculation assumes that all dividends and distributions, if any, have been reinvested. Total return does not reflect broker commissions or sales charges in connection with the purchase or sale of Fund shares and includes the effect of any expense reductions, if any. Total return for a period of less than one year is not annualized.

Performance at market price will differ from results at NAV. Although market price returns typically reflect investment results over time, during shorter periods returns at market price can also be influenced by factors such as changing views about the Fund, market conditions, supply and demand for the Fund’s shares, or changes in the Fund’s dividends.

An investment in the Fund involves risk, including the loss of principal. Total return, market price, market price yield and NAV will fluctuate with changes in market conditions. This data is provided for information purposes only and is not intended for trading purposes. Closed-end funds, unlike open-end funds, are not continuously offered. There is a one-time public offering and once issued, shares of closed-end funds are traded in the open market through a stock exchange. NAV is equal to total assets attributable to common shareholders less total liabilities divided by the number of common shares outstanding. Holdings are subject to change daily.

(2) The NAV disclosed in the Fund’s financial statements may differ due to accounting principles generally accepted in the United States of America.

(3) Market Price Yield is determined by dividing the annualized current (declared February 1, 2016) monthly dividend per common share (comprised of net investment income and net capital gains, if any) by the market price per common share at January 31, 2016.

(4) Represents Mandatory Redeemable Preferred Shares outstanding, Senior Secured Notes outstanding and amounts drawn under the short-term margin loan facility (“Leverage”), as a percentage of total managed assets. Total managed assets refer to total assets (including assets attributable to Leverage) minus liabilities (other than liabilities representing Leverage).

10 Annual Report | January 31, 2016

Performance & Statistics

AllianzGI Equity & Convertible Income Fund

January 31, 2016 (unaudited)

(1) Past performance is no guarantee of future results. Total return is calculated by determining the percentage change in NAV or market price (as applicable) in the specified period. The calculation assumes that all dividends and distributions, if any, have been reinvested. Total return does not reflect broker commissions or sales charges in connection with the purchase or sale of Fund shares and includes the effect of any expense reductions, if any. Total return for a period of more than one year represents the average annual total return.

Performance at market price will differ from results at NAV. Although market price returns typically reflect investment results over time, during shorter periods returns at market price can also be influenced by factors such as changing views about the Fund, market conditions, supply and demand for the Fund’s shares, or changes in the Fund’s dividends.

An investment in the Fund involves risk, including the loss of principal. Total return, market price, market price yield and NAV will fluctuate with changes in market conditions. This data is provided for information purposes only and is not intended for trading purposes. Closed-end funds, unlike open-end funds, are not continuously offered. There is a one-time public offering and once issued, shares of closed-end funds are traded in the open market through a stock exchange. NAV is equal to total assets less total liabilities divided by the number of shares outstanding. Holdings are subject to change daily.

(2) The NAV disclosed in the Fund’s financial statements may differ due to accounting principles generally accepted in the United States of America.

(3) Market Price Yield is determined by dividing the annualized current quarterly dividend per share (comprised of net investment income and net capital gains, if any) by the market price per share at January 31, 2016.

January 31, 2016 | Annual Report 11

Performance & Statistics

AllianzGI NFJ Dividend, Interest & Premium Strategy Fund

January 31, 2016 (unaudited)

(1) Past performance is no guarantee of future results. Total return is calculated by determining the percentage change in NAV or market price (as applicable) in the specified period. The calculation assumes that all dividends and distributions, if any, have been reinvested. Total return does not reflect broker commissions or sales charges in connection with the purchase or sale of Fund shares and includes the effect of any expense reductions, if any. Total return for a period of more than one year represents the average annual total return.

Performance at market price will differ from results at NAV. Although market price returns typically reflect investment results over time, during shorter periods returns at market price can also be influenced by factors such as changing views about the Fund, market conditions, supply and demand for the Fund’s shares, or changes in the Fund’s dividends.

An investment in the Fund involves risk, including the loss of principal. Total return, market price, market price yield and NAV will fluctuate with changes in market conditions. This data is provided for information purposes only and is not intended for trading purposes. Closed-end funds, unlike open-end funds, are not continuously offered. There is a one-time public offering and once issued, shares of closed-end funds are traded in the open market through a stock exchange. NAV is equal to total assets less total liabilities divided by the number of shares outstanding. Holdings are subject to change daily.

(2) The NAV disclosed in the Fund’s financial statements may differ due to accounting principles generally accepted in the United States of America.

(3) Market Price Yield is determined by dividing the annualized current quarterly dividend per share (comprised of net investment income and net capital gains, if any) by the market price per share at January 31, 2016.

12 Annual Report | January 31, 2016

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016

January 31, 2016 | Annual Report 13

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (continued)

14 Annual Report | January 31, 2016

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (continued)

January 31, 2016 | Annual Report 15

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (continued)

16 Annual Report | January 31, 2016

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (continued)

January 31, 2016 | Annual Report 17

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (continued)

18 Annual Report | January 31, 2016

Schedule of Investments

AllianzGI Diversified Income & Convertible Fund

January 31, 2016 (continued)