Principle Of Equivalent Utility Research Articles

Characterization of positive homogeneity for the principle of equivalent utility

Characterization of positive homogeneity for the principle of equivalent utility

On Extendability of the Principle of Equivalent Utility

An insurance premium principle is a way of assigning to every risk a real number, interpreted as a premium for insuring risk. There are several methods of defining the principle. In this paper, we deal with the principle of equivalent utility under the rank-dependent utility model. The principle, generated by utility function and probability distortion function, is based on the assumption of the symmetry between the decisions of accepting and rejecting risk. It is known that the principle of equivalent utility can be uniquely extended from the family of ternary risks. However, the extension from the family of binary risks need not be unique. Therefore, the following problem arises: characterizing those principles that coincide on the family of all binary risks. We reduce the problem thus to the multiplicative Pexider functional equation on a region. Applying the form of continuous solutions of the equation, we solve the problem completely.

Indifference pricing of a life insurance portfolio with risky asset driven by a shot-noise process

In this paper, we investigate the pricing problem for a portfolio of life insurance contracts where the life contingent payments are equity-linked depending on the performance of a risky stock or index. The shot-noise effects are incorporated in the modeling of stock prices, implying that sudden jumps in the stock price are allowed, but their effects may gradually decline over time. The contracts are priced using the principle of equivalent utility. Under the assumption of exponential utility, we find the optimal investment strategy and show that the indifference premium solves a non-linear partial integro-differential equation (PIDE). The Feynman–Kač form solutions are derived for two special cases of the PIDE. We further discuss the problem for the asymptotic shot-noise process, and find the probabilistic representation of the indifference premium. We also provide some numerical examples and analyze parameter sensitivities for the results obtained in this paper.

Indifference Pricing of a GLWB Option in Variable Annuities

We investigate the valuation problem of variable annuities with guaranteed lifelong/lifetime withdrawal benefit (GLWB) options, which give the policyholder the right to withdraw a specified amount as long as he or she lives, regardless of the performance of the investment. We assume the static approach that the policyholder’s withdrawal rate is a constant throughout the life of the contract. We apply the principle of equivalent utility to find the indifference price for a variable annuity with a GLWB contract with an equity-indexed death benefit. Using an exponential utility function, Hamilton-Jacobi-Bellman (HJB) type partial differential equations (PDEs) are derived for the pricing functions. We first assume the mortality is deterministic, and the pricing PDE is solved numerically using a finite difference method. The effects of various parameters are investigated, including the age at inception of the policyholder, withdrawal rate, risk-free rate, and volatility of the underlying asset. We also consider a roll-up option and analyze the effect of delaying the start of the withdrawals. Another pricing PDE is derived with a stochastic mortality, when the force of mortality is modeled with a stochastic differential equation. A finite difference method is used again to solve the pricing PDE numerically, and the sensitivities of the GLWB contracts with respect to the withdrawal rate and the risk-free rate are explored.

Positive Homogeneity of the Principle of Equivalent Utility

Positive Homogeneity of the Principle of Equivalent Utility

Scale Invariance of Principle of Equivalent Utility under Cumulative Prospect Theory

Scale Invariance of Principle of Equivalent Utility under Cumulative Prospect Theory J. Chudziaka∗, M. Halicki, S. Wojcik Faculty of Mathematics and Natural Sciences, University of Rzeszow, Prof. St. Pigonia 1, 35-310 Rzeszow, Poland Department of Regional Politics and Food Economy, University of Rzeszow, Cwiklinskiej 2, 35-601 Rzeszow, Poland Statistical Office in Rzeszow, Jana III Sobieskiego 10, 35-959 Rzeszow, Poland

A Markov Process Modeling and Analysis of Indifference Pricing of Insurance Contracts for Home Reversion Plan for a Pair of Insureds

The intent of the home reversion plan for retired homeowners in United Kingdom is to help house-rich but cash-poor seniors by the way of releasing their home equity into cash so as to meet living expenses and continue to enjoy the right to live in their home until their death. We present multiple finite state Markov models to price the continuous annuities of insurance policies relevant to home reversion plan for a pair of insureds (meaning husband and wife). Our modeling assumes that the home value follows a geometric Brownian motion. By applying the principle of equivalent utility, we derive the partial differential equation system that the indifferent annuities satisfy under the exponential utility function, and find their explicit representations. Furthermore, we employ an explicit finite difference scheme to calculate the numerical solution and discuss the impacts of the risk aversion of insurer, the volatility of home value, and the interest rate on the annuities of home reversion plan for a couple. We observe that these results reflect our intuition.

Pricing a contract of linking home reversion plan and long-term care insurance via the principle of equivalent utility

Home reversion plans allow homeowners to tap into the value of their house and live in it until their death. The article considers a contract linking home reversion plan and long-term care insurance, which could better prepare seniors for their retirement and long-term care needs. Here, we assume the product exposes an insurer to two risks: the uncertainty of nursing care cost from disable, and the home value decreasing in real estate markets at the time of sale. Because the market is incomplete, we apply the principle of equivalent utility to price the contract under exponential utility.

Indifference pricing of a life insurance portfolio with systematic mortality risk in a market with an asset driven by a Lévy process

In this paper, we investigate the problem of pricing and hedging of life insurance liabilities. We consider a financial market consisting of a risk-free asset with a constant rate of return, and a risky asset whose price is driven by a Lévy process. We take into account a systematic mortality risk and model mortality intensity as a diffusion process. The principle of equivalent utility is chosen as the valuation rule. In order to solve our optimization problems, we apply techniques from the stochastic control theory. An exponential utility is considered in detail. We arrive at three pricing equations and investigate some properties of the premiums. An estimate of the finite-time ruin probability is derived. Indifference pricing with respect to a quadratic loss function is also briefly discussed.

Principle of equivalent utility and universal variable life insurance pricing

In this paper we study the pricing problem for a class of universal variable life (UVL) insurance products, using the idea of principle of equivalent utility. As the main features of UVL products we allow the (death) benefit to depend on certain indices or assets that are not necessarily tradable (e.g., pension plans), and we also consider the “multiple decrement” cases in which various status of the insured are allowed and the benefit varies in accordance with the status. Following the general theory of indifference pricing, we formulate the pricing problem as stochastic control problems, and derive the corresponding HJB equations for the value functions. In the case of exponential utilities, we show that the prices can be expressed explicitly in terms of the global, bounded solutions of a class of semilinear parabolic PDEs with exponential growth. In the case of general insurance models where multiple decrements and random time benefit payments are all allowed, we show that the price should be determined by the solutions to a system of HJB equations, each component corresponds to the value function of an optimization problem with the particular status of the insurer.

Pricing equity-linked pure endowments with risky assets that follow Lévy processes

We investigate the pricing problem for pure endowment contracts whose life contingent payment is linked to the performance of a tradable risky asset or index. The heavy tailed nature of asset return distributions is incorporated into the problem by modeling the price process of the risky asset as a finite variation Lévy process. We price the contract through the principle of equivalent utility. Under the assumption of exponential utility, we determine the optimal investment strategy and show that the indifference price solves a non-linear partial-integro-differential equation (PIDE). We solve the PIDE in the limit of zero risk aversion, and obtain the unique risk-neutral equivalent martingale measure dictated by indifference pricing. In addition, through an explicit–implicit finite difference discretization of the PIDE we numerically explore the effects of the jump activity rate, jump sizes and jump skewness on the pricing and the hedging of these contracts.

Pricing equity-linked pure endowments via the principle of equivalent utility

We consider a pure endowment contract whose life contingent payout is linked to the performance of a risky stock or index. Because of the additional mortality risk, the market is incomplete; thus, a fundamental assumption of the Black–Scholes theory is violated. We price this contract via the principle of equivalent utility and demonstrate that, under the assumption of exponential utility, the indifference price solves a nonlinear Black–Scholes equation; the nonlinear term reflects the mortality risk and exponential risk preferences in our model. We discuss qualitative and quantitative properties of the premium, including analytical upper and lower bounds.