A pseudo-analytic generalization of the memoryless property for continuous random variables and its use in pricing contingent claims

Peter Carr; Pasquale Cirillo

doi:10.1098/rsos.231690

A pseudo-analytic generalization of the memoryless property for continuous random variables and its use in pricing contingent claims

R Soc Open Sci. 2024 Apr 10;11(4):231690. doi: 10.1098/rsos.231690. eCollection 2024 Apr.

Authors

Peter Carr¹, Pasquale Cirillo²

Affiliations

¹ Finance and Risk Engineering Department, New York University, New York, NY, USA.
² ZHAW School of Management and Law, Institute of Business Information Technology, Winterthur, Switzerland.

Abstract

We explore an extension of the memoryless property for continuous random variables by using the concept of pseudo-sum. Subsequently, we demonstrate the practicality of this approach through two financial applications in which pseudo-sums characterize the values of arbitrage-free contingent claims. Moreover, we are able to establish new interesting connections between different probability distributions.

Keywords: contingent claim; distribution theory; memoryless property; pseudo-analysis; pseudo-sum.