Martingale measures for the geometric Lévy process models
نویسنده
چکیده
The equivalent martingale measures for the geometric Lévy processes are investigated. They are separated to two groups. One is the group of martingale measures which are obtained by Esscher transform. The other one is such group that are obtained as the minimal distance martingale measures. We try to obtain the explicit forms of the martingale measures, and we compare the properties of the martingale measures to each other. Those discussions help for us to do the fitness analysis of the pricing models.
منابع مشابه
Optimal investment in a Lévy Market∗
The stock price process is modelled by a geometric Lévy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However the model can be completed by the so called power-jump assets. By doing this we allow investment in these new assets and we can try t...
متن کاملA Note on Esscher Transformed Martingale Measures for Geometric Lévy Processes
The Esscher transform is one of the very useful methods to obtain the reasonable equivalent martingale measures, and it is defined with relation to the corresponding risk process. In this article we consider two kinds of risk processes (compound return process and simple return process). Then we obtain two kinds of Esscher transformed martingale measures. The first one is the one which was intr...
متن کاملSome problems of portfolio optimization and hedging in a Lévy market via fictitious completions
The classical Merton’s problem of utility maximization was recently solved in [2] in a market consisting of a bond with constant interest rate, a stock that follows a geometric Lévy model, and certain “fictitious” stocks called powerjump assets. Using their previous work [3] on the completeness of such a market and the martingale method, it was proved there that for certain utility functions, i...
متن کاملA Martingale Representation for the Maximum of a Lévy Process
By using Malliavin calculus for Lévy processes, we compute an explicit martingale representation for the maximum of a square-integrable Lévy process.
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