Thus absolute risk aversion measure is given by Here Y is the risk aversion coefficient. Users should refer to the original published version of the material for the full abstract. (d) The Power Utility Function: Thus U’ (W) W -1 and U (W) ( 1 )W -2 This means that for the power utility function to satisfy the principle of non-satiation and diminishing marginal utility of wealth (risk aversion) we require < 1. No warranty is given about the accuracy of the copy. However, users may print, download, or email articles for individual use. The latter formed the basis for the development of power util- ity functions, as indicated in At-Sahalia and Brandt (2001). A novel concept called power utility is proposed to elaborately. Copyright of Engineering Letters is the property of Newswood Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. Inspired by utility theory in economics, a unified framework of user satisfaction is proposed.Finally, the numerical simulations are presented to show the effects of model parameters on the insurer's optimal reinsurance and investment strategies. The explicit expressions for optimal reinsurance-investment strategy and value function are determined by the stochastic approach, which uses the equations of Hamilton-Jacobi-Bellman. The insurer's objective is to maximize the expected fractional power utility from terminal wealth. Assuming that the insurer surplus process is approximated by Brownian motion with drift, the insurer may purchase reinsurance and invest the capital in a financial market consisting of risk-free asset and risk asset whose price is modeled by constant elasticity variance (CEV) model. Abstract: This paper studies the optimal reinsurance and investment problem for insurance companies (insurers) with a fractional power utility function. We will use these utility functions both in portfolio choice and in pricing we start by discussing utility.
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