Optimal Design of a Perpetual Equity-Indexed Annuity

Moore, Kristen S.; Young, Virginia R.

doi:10.1080/10920277.2005.10596184

Cited by 11 publications

(15 citation statements)

References 19 publications

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“…This case was considered in Moore and Young (2005); however, in that paper, we restricted our analysis to the case in which the no-surrender region is an interval (w l , w u ); i.e., the case in which there are lower and upper surrender thresholds w l and w u . In this section, we discuss cases for which there is no lower surrender threshold w l .…”

Section: Definition Of the Value Functionsmentioning

confidence: 99%

“…We refer the reader to Section 2.1 of Moore and Young (2005) for a discussion of the smoothness of solutions to (7). Standard verification theorems ensure that if (7) has a smooth solution V , then it equals the value function as defined in (6) and one can recover the the optimal investment strategy π * t from the first order condition in (7).…”

Section: Definition Of the Value Functionsmentioning

confidence: 99%

“…We choose the following as our base scenario; it is similar to the base scenario studied in Moore and Young (2005).…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In that paper, we gave an algorithm for solving the system. The key step in the algorithm was finding a root x = wu w 0 of a function η that may assume real or complex values; see equations (2.31) and (2.32) in Moore and Young (2005). In this section, we consider cases for which the method of Moore and Young (2005) fails; i.e., cases for which η has no real root (and hence the system of six equations in six unknowns has no solution).…”

Section: Definition Of the Value Functionsmentioning

confidence: 99%

“…More specifically, we consider an investor who seeks to maximize her expected utility of bequest (or wealth at death) and study the optimal time to surrender the EIA contract, assuming that she allocates her assets optimally, in the sense of Merton (1992), after surrendering the contract. Moore and Young (2005) considered a similar problem for a perpetual EIA with time-homogeneous benefits under the assumption of constant hazard rate (i.e., exponential future lifetime). In that paper, we limited our study of the optimal strategies to the case in which lower and upper surrender thresholds exist.…”

Section: Introductionmentioning

confidence: 99%

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Optimal surrender strategies for equity-indexed annuity investors

Moore

2009

Insurance: Mathematics and Economics

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An equity-indexed annuity (EIA) is a hybrid between a variable and a fixed annuity that allows the investor to participate in the stock market and earn at least a minimum interest rate. The investor sacrifices some of the upside potential for the downside protection of the minimum guarantee. Because EIAs allow investors to participate in equity growth without the downside risk, their popularity has grown rapidly.An optimistic EIA owner might consider surrendering an EIA contract, paying a surrender charge, and investing the proceeds directly in the index to earn the full (versus reduced) index growth, while using a risk-free account for downside protection. Because of the popularity of these products, it is important for individuals and insurers to understand the optimal policyholder behavior.We consider an EIA investor who seeks the surrender strategy and post-surrender asset allocation strategy that maximize the expected discounted utility of bequest. We formulate a variational inequality and a Hamilton-Jacobi-Bellman equation that govern the optimal surrender strategy and post-surrender asset allocation strategy, respectively. We examine the optimal strategies and how they are affected by the product features, model parameters, and mortality assumptions. We observe that in many cases, the "no-surrender" region is an interval (w l , w u ); i.e., that there are two free boundaries. In these cases, the investor surrenders the EIA contract if the fund value becomes too high or too low. In other cases, there is only one free boundary; the lower (or upper) surrender threshold vanishes. In these cases, the investor holds the EIA, regardless of how low (or high) the fund value goes. For a special case, we prove a succinct and intuitive condition on the model parameters that dictates whether one or two free boundaries exist.

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Section: Definition Of the Value Functionsmentioning

confidence: 99%

Section: Definition Of the Value Functionsmentioning

confidence: 99%

“…We choose the following as our base scenario; it is similar to the base scenario studied in Moore and Young (2005).…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Definition Of the Value Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal surrender strategies for equity-indexed annuity investors

Moore

2009

Insurance: Mathematics and Economics

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Pricing life insurance contracts with early exercise features

Bacinello

Biffis

Millossovich

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this paper we describe an algorithm based on the Least Squares Monte Carlo method to price life insurance contracts embedding American options. We focus on equity-linked contracts with surrender options and terminal guarantees on benefits payable upon death, survival and surrender. The framework allows for randomness in mortality as well as stochastic volatility and jumps in financial risk factors. We provide numerical experiments demonstrating the performance of the algorithm in the context of multiple risk factors and exercise dates.

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Optimal stopping behavior of equity-linked investment products with regime switching

Cheung

Yang

2005

Insurance: Mathematics and Economics

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Optimal Design of a Perpetual Equity-Indexed Annuity

Cited by 11 publications

References 19 publications

Optimal surrender strategies for equity-indexed annuity investors

Optimal surrender strategies for equity-indexed annuity investors

Pricing life insurance contracts with early exercise features

Optimal stopping behavior of equity-linked investment products with regime switching

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