Game pricing and double sequence of random variables

TL;DR

This paper investigates optimal investment strategies in a game with potentially infinite expected returns, introducing a novel pricing method that differs from the Black-Scholes formula to maximize growth rate.

Contribution

It proposes a new pricing approach for games with infinite expectation, optimizing investment proportions to maximize long-term growth.

Findings

Derived optimal investment proportions for infinite expectation games

Developed a new pricing method distinct from Black-Scholes

Demonstrated improved growth rate maximization strategies

Abstract

In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing method in which the price is different from that obtained by the Black-Scholes formula for a European option.