Minimal Entropy Martingale Measures of Jump Type Price Processes in Incomplete Assets Markets

We consider the incomplete assets market and assume that the market has no-arbitrage. Then there are many equivalent martingale measures associated with the market. Among them, a probability measure which minimizes the relative entropy with respect to the original probability measure P, has a special importance. Such a measure is called the minimal entropy martingale measure (MEMM). In a previous paper, we have proved the existence theorem of the MEMM for the price processes given in the form of the diffusion type stochastic differential equation. In this article we discuss the MEMM of the jump type price processes, or especially of the log Lévy processes, and we give the explicit form of MEMM.     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.     

[Geometric Lévy Process & MEMM] Pricing Model and Related Estimation Problems

In this article the [Geometric Lévy Process & MEMM] pricingmodel is proposed. This model is an option pricing model for theincomplete markets, and this model is based on the assumptions that theprice processes are geometric Lévy processes and that the pricesof the options are determined by the minimal relative entropy methods.This model has many good points. For example, the theoretical part ofthe model is contained in the framework of the theory of Lévyprocess (additive process). In fact the price process is also aLévy process (with changed Lévy measure) under the minimalrelative entropy martingale measure (MEMM), and so the calculation ofthe prices of options are reduced to the computation of functionals ofLévy process. In previous papers, we have investigated thesemodels in the case of jump type geometric Lévy processes. In thispaper we extend the previous results for more general type of geometricLévy processes. In order to apply this model to real optionpricing problems, we have to estimate the price process of theunderlying asset. This problem is reduced to the estimation problem ofthe characteristic triplet of Lévy processes. We investigate thisproblem in the latter half of the paper.     

Both Sensitive Value Measure and its Applications

Asia-Pacific Financial Markets - In this paper we introduce the both sensitive value measure, which is an extended value measure of the risk sensitive value measure. We also introduce...