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Initial Wealth (initial + wealth)
Selected AbstractsUtility Functions whose Parameters depend on Initial WealthBULLETIN OF ECONOMIC RESEARCH, Issue 4 2003Christian S. Pedersen D81; G11 Abstract Conventional one-period utility functions in Economics assume that initial wealth only enters preferences through the definition of final wealth. Consequently, those utility functions most utilized (i.e., exponential and quadratic) have implausible risk characteristics. The authors characterize a new class of utility function whose risk parameters depend upon initial wealth and obtain several desirable results. In particular, investors with quadratic and exponential utility functions can have decreasing risk aversion, and risky assets in a quadratic utility multi-asset environment do not have to be inferior as implied by the traditional framework. [source] Comonotonic Approximations for Optimal Portfolio Selection ProblemsJOURNAL OF RISK AND INSURANCE, Issue 2 2005J. Dhaene We investigate multiperiod portfolio selection problems in a Black and Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of "constant mix" portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari's dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene et al. (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically. [source] Randomized Stopping Times and American Option Pricing with Transaction CostsMATHEMATICAL FINANCE, Issue 1 2001Prasad Chalasani In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surprising feature of our upper hedging price representation is that it requires the use of randomized stopping times (Baxter and Chacon 1977), just as ordinary stopping times are needed in the absence of transaction costs. We also represent the upper hedging price as the optimum value of a variety of optimization problems. Additionally, we show a two-player game where at Nash equilibrium the value to both players is the upper hedging price, and one of the players must in general choose a mixture of stopping times. We derive similar representations for the lower hedging price as well. Our results make use of strong duality in linear programming. [source] Utility Functions whose Parameters depend on Initial WealthBULLETIN OF ECONOMIC RESEARCH, Issue 4 2003Christian S. Pedersen D81; G11 Abstract Conventional one-period utility functions in Economics assume that initial wealth only enters preferences through the definition of final wealth. Consequently, those utility functions most utilized (i.e., exponential and quadratic) have implausible risk characteristics. The authors characterize a new class of utility function whose risk parameters depend upon initial wealth and obtain several desirable results. In particular, investors with quadratic and exponential utility functions can have decreasing risk aversion, and risky assets in a quadratic utility multi-asset environment do not have to be inferior as implied by the traditional framework. [source] | ||||||||||