Optimal Surrender Research Articles

Risk Management of Policyholder Behavior in Equity‐Linked Life Insurance

AbstractThe financial guarantees embedded in variable annuity contracts expose insurers to a wide range of risks, lapse risk being one of them. When policyholders’ lapse behavior differs from the assumptions used to hedge variable annuity contracts, the effectiveness of dynamic hedging strategies can be significantly impaired. By studying how the fee structure and surrender charges affect surrender incentives, we obtain new theoretical results on the optimal surrender region and use them to design a marketable contract that is never optimal to lapse.

A Study of the Effect of Income Risk on the Optimal Insurance Contract and Surrender Value

A Study of the Effect of Income Risk on the Optimal Insurance Contract and Surrender Value

Risk Management of Policyholder Behavior in Equity Linked Life Insurance

The financial guarantees embedded in variable annuity (VA) contracts expose insurers to a wide range of risks, lapse risk being one of them. When policyholders' lapse behavior differs from the assumptions used to hedge VA contracts, the effectiveness of dynamic hedging strategies can be significantly impaired. By studying how the fee structure and surrender charges affect surrender incentives, we obtain new theoretical results on the optimal surrender region and use them to design a marketable contract that is never optimal to lapse.

Optimal surrender policy for variable annuity guarantees

This paper proposes a technique to derive the optimal surrender strategy for a variable annuity (VA) as a function of the underlying fund value. This approach is based on splitting the value of the VA into a European part and an early exercise premium following the work of Kim and Yu (1996) and Carr et al. (1992). The technique is first applied to the simplest VA with GMAB (path-independent benefits) and is then shown to be possibly generalized to the case when benefits are path-dependent. Fees are paid continuously as a fixed percentage of the fund value. Our approach is useful to investigate the impact of path-dependent benefits on surrender incentives.

Optimal Surrender Policy for Variable Annuity Guarantees

This paper proposes a technique to derive the optimal surrender strategy for a variable annuity (VA) as a function of the underlying fund value. This approach is based on splitting the value of the VA into a European part and an early exercise premium following the work of Kim and Yu (1996) and Carr, Jarrow and Myneni (1992). The technique is first applied to the simplest VA with GMAB (path-independent benefits) and is then shown to be possibly generalized to the case when benefits are path-dependent. Fees are paid continuously as a fixed percentage of the fund value. Our approach is useful to investigate the impact of path-dependent benefits on surrender incentives.

Optimal surrender strategies for equity-indexed annuity investors with partial information

In this paper we consider an equity-indexed annuity (EIA) investor who wants to determine when he should surrender the EIA in order to maximize his logarithmic utility of the wealth at surrender time. We model the dynamics of the index using a geometric Brownian motion with regime switching. To be more realistic, we consider a finite time horizon and assume that the Markov chain is unobservable. This leads to the optimal stopping problem with partial information. We give a representation of the value function and an integral equation satisfied by the boundary. In the Bayesian case which is a special case of our model, we obtain analytical results for the value function and the boundary.

Optimal surrender strategies for equity-indexed annuity investors

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 maximizes 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.

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

In recent years, there is a growing interest in equity-linked investment products. The return credited to such product depends on the return of some underlying reference index. A prominent example is the equity-indexed annuities (EIAs). A special feature of many of the equity-linked products is that the holders are entitled the right to surrender the product prior to maturity. In this paper, we will study the optimal surrender time for a equity-linked product in a discrete-time setting. We assume that the market environment will switch among different regimes in a Markovian way, and the return of the reference index will have different distributions in different regimes. Assuming a CRRA preference, we have obtained the optimal surrender policy. Properties of the optimal surrender behavior, in particular the effect of regime switching, are examined.