Some Applications in Economy for Utility Functions Involving Risk Theory
Abstract We present in the first part of the article types of utility functions that can describe the behavior of the investor and their applications to optimize portfolio. The second part of the paper refers to applications in calculating insurance premiums aggregated risk in zero utility principle.
An Introduction to Utility Theory
A gentle but reasonably rigorous introduction to utility theory. Utility functions give us a way to measure investor’s preferences for wealth and the amount of risk they are willing to undertake in the hope of attaining greater wealth. This makes it possible to develop a theory of portfolio optimization. Thus utility theory lies at the heart of modern portfolio theory. We develop the basic concepts of the theory through a series of simple examples. We discuss non-satiation, risk aversion, the principle of expected utility maximization, fair bets, certainty equivalents, portfolio optimization, coecients of risk aversion, iso-elasticity, relative risk aversion, and absolute risk aversion.
Continuous-Time Finance
Section I: Introductin to Finance and the Mathematics of Continuous-Time Models 1 Modern Finance 2 Introduction to Portfolio Selection and Capital Market Theory: Static Analysis 3 On the Mathematics and Economic Assumptions of Continuous-Time Financial Models Section II: Optimum Consumption and Portfolio Selection in Continuous-Time Models 4. Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 5. Optimum Consumption and Portfolio Rules in a Continuous-Time Model 6. Further Developments in theory of Optimal Consumption and Portfolio Selection Section III: Warrant and Option Pricing Theory 7. A Complete Model of Warrant Pricing the Maximizes Utility 8. Theory of Rational Option Pricing 9. Option Pricing when Underlying Stock Returns are Discontinuous 10. Further Developments in Option Pricing Theory Section IV: Contingent-Claims Analysis in the Theory of Corporate Finance and Financial Intermediation 11. A Dynamic General Equilibrium Model of the Asset Market and its Application to the Pricing of the Capital Structure of the Firm 12. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates 13. On the Pricing of Contingent Claims and the Modigliani-Miller Theorem 14. Contingent Claims Analysis in the Theory of Corporate Finance and Financial Intermediation Section V: An Intertemporal-Equilibrium Theory of Finance 15. An Intertemporal Capital Asset Pricing Model 16. A General Equilibrium Theory of Finance in Continuous-Time Section VI: Applications of the Continuous-Time Model to Selected Issues in Public Finance 17. An Asymptotic Theory of Growth Under Uncertainty 18. On Consumption-Indexed Public Pension Plans 19. An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance 20. On the Cost of Deposit Insurance when there are Surveillance Costs