Pricing equity-linked pure endowments with risky assets that follow Lévy processes. (English) Zbl 1242.60069
Summary: 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 explicitimplicit 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.
MSC:
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60G51 | Processes with independent increments; Lévy processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 91G80 | Financial applications of other theories |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
Equity-linked pure endowments; Equity indexed annuities; Indifference pricing; Exponential utility; Lévy processes; Heavy tailed distributionReferences:
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