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A bold strategy is not always optimal in the presence of inflation. (English) Zbl 1057.60036

A modification of the primitive casino considered by L. E. Dubins and L. J. Savage [“How to gamble if you must. Inequalities for stochastic processes” (1965; Zbl 0133.41402)] is formulated. The model is designed to handle inflation and to motivate the gambler to recognize the time value of money. It forces to complete the game as quickly as the goal is reached. The goal is to buy a house which sells today for \(y\) dollars suppose that you own \(x\) dollars (\(y>x>0\)). A famous result is that in the subfair and fair primitive casinos, when there are no inflation, an optimal strategy is bold play whereby at each trial the player bets \(\min (x,1-x)\) [see R. W. Chen, Z. Wahrscheinlichkeitstheorie Verw. Geb. 42, 293–301 (1978; Zbl 0362.60067)]. It is shown that for subfair and fair primitive casinos, in the case of a positive inflation rate \(\alpha\), it may not be optimal to play boldly.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60K99 Special processes
91A60 Probabilistic games; gambling
62L15 Optimal stopping in statistics
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References:

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