An Exponential Martingale Equation
نویسنده
چکیده
We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.
منابع مشابه
Risk measurement and Implied volatility under Minimal Entropy Martingale Measure for Levy process
This paper focuses on two main issues that are based on two important concepts: exponential Levy process and minimal entropy martingale measure. First, we intend to obtain risk measurement such as value-at-risk (VaR) and conditional value-at-risk (CvaR) using Monte-Carlo methodunder minimal entropy martingale measure (MEMM) for exponential Levy process. This Martingale measure is used for the...
متن کاملStochastic functional population dynamics with jumps
In this paper we use a class of stochastic functional Kolmogorov-type model with jumps to describe the evolutions of population dynamics. By constructing a special Lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...
متن کاملThe Minimal Entropy Martingale Measure and Hedging in Incomplete Markets
The intent of these essays is to study the minimal entropy martingale measure, to examine some new martingale representation theorems and to discuss its related Kunita-Watanabe decompositions. Such problems arise in mathematical finance for an investor who is confronted with the issues of pricing and hedging in incomplete markets. We adopt the standpoint of a ra tional investor who principally...
متن کاملDERIVATIVES PRICING VIA p-OPTIMAL MARTINGALE MEASURES: SOME EXTREME CASES
In an incomplete financial market in which the dynamics of the asset prices is driven by a d-dimensional continuous semimartingale X, we consider the problem of pricing European contingent claims embedded in a power utility framework. This problem reduces to identifying the p-optimal martingale measure, which can be given in terms of the solution to a semimartingale backward equation. We use th...
متن کاملPower Utility Maximization in Constrained Exponential Lévy Models
We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences...
متن کامل