3/14/2023 0 Comments Power utility function![]() ![]() ![]() As by-products, the option-pricing formula of Black-Scholes can be derived and the Esscher method of option pricing can be explained. The second is the economic equilibrium originally proposed by Borch. ![]() The first, believed to be new, is based on the synergy potential this is the largest amount that can be withdrawn from the system without hurting any company in terms of expected utility. Utility of Consumption and Certainty-Equivalent Value Marginal Satisfaction of eating cookies is a diminishing function Hence, Accumulated Satisfaction is a concave function Accumulated Satisfaction represents Utility of Consumption U(x) Where x represents the uncertain outcome being consumed Degree of concavity represents extent of our Risk. The family of Pareto optimal risk exchanges is characterized by the theorem of Borch. They are interested in exchanging wealth to improve their expected utility. Then n companies (or economic agents) with random wealth are considered. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the. The postulate of equivalent expected utility can be used to replace a random gain by a fixed amount and to determine a fair premium for claims to be insured, even if the insurer’s wealth without the new contract is a random variable itself. This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility function). This article is a self-contained survey of utility functions and some of their applications. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |