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The p-Optimal Martingale Measure and Its Asymptotic Relation with the Minimal-Entropy Martingale Measure

Peter Grandits

Open publisher page 40 citations

Abstract

We prove convergence of the p-optimal martingale measures to the minimal-entropy martingale measure for p →1. This is done for bounded stochastic processes in a discrete-time setting with a finite horizon. We also investigate in detail an example of an unbounded process, where we do not find this convergence.

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What this paper is about

We prove convergence of the p-optimal martingale measures to the minimal-entropy martingale measure for p →1. This is done for bounded stochastic processes in a discrete-time setting with a finite horizon. We also investigate in detail an example of an unbounded process, where we do not find this convergence.

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OpenAlex reports 40 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove convergence of the p-optimal martingale measures to the minimal-entropy martingale measure for p →1. This is done for bounded stochastic processes in a discrete-time setting with a finite horizon. We also investigate in detail an example of an unbounded process, where we do not find this convergence.

Key concepts: Mathematics, Doob's martingale inequality, Martingale pricing, Martingale (probability theory), Local martingale, Martingale difference sequence, Applied mathematics, Pure mathematics

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