GENERALISED OPTIMAL STOPPING STRATEGIES WITH APPLICATIONS TO FINANCE

Abstract

In this paper we examine the problem of determining the best time to sell an asset, where the stock price is modelled by a hybrid process. In this paper hybrid variable is a mathematical concept that is used to describe a situation in which randomness and fuzziness simultaneously appear in a system or phenomenon. Based on this concept, a hybrid stopping time problem is formulated and investigated. A verification theorem is derived and proved. We illustrate the application of the verification theorem through a practical example in mathematics of finance. A power function with exponent , is used as the utility function in the example. This study is extending the model from Oksendal [12] by including the fuzzy component since market value of assets is usually described using vague human language. The theory of hybrid variables provides a more realistic description of the evolution of price processes of financial assets.

Keywords: Randomness, fuzziness, Fuzzy variable, fuzzy process, hybrid variable, hybrid process, stopping time.