Communications in Mathematical Finance

Gamblerís Risk of Ruin and Optimal Bet

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  • Abstract 
    Classical study of betting and gambling largely argues that, individual is able to make more revenue from a fraction of income wagered, with utility of pleasure for participation being minimal. This explains why, unlike insurance, where people resort to reduce the impact of risk, gambling is sought to bear risk (Ankomah 2015).  Reasonably so, the gain in revenue is a proximate avenue for a person to place bets to buy and bear risk of such fluctuated nature. However, inherent in this decision making lie the risk of ruin (RoR) that stares the gambler as he/she struggles to earn an expected level of income from a given bankroll. Akin to the gamblerís RoR is the optimal stopping time. The paper discusses the best point of exit for the gambler, and further derives and analyse the possible RoR of the gambler relative to the randomness and uncertain nature that characterise the game of gambling, and further considers the optimal betting strategy, whiles suggesting the best point of exit using Waldís equation. It was found that, the ruin of the gambler at any point in time remains eminent with the randomness of the game of betting and gambling. It was concluded that, optimal betting strategy exists for the adoption of bettors relative to the amount for wagering and best point of exit for reason of ruin avoidance.  
    Keywords: Gamblerís Ruin, Probability of Ruin, Random walk, stopping time, Waldís Equation.