An equivalent martingale measure selection strategy for discrete time, continuous state, asset price evolution models is proposed. The minimal martingale law is shown to generally fail to produce a probability law in this context. The proposed strategy, termed the Girsanov principle, performs a multiplicative decomposition of asset price movements into a predictable and martingale component wit...

We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P ⋆ which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P ⋆ coincides with the variance-optimal martin-gale measure relative to the original probability measure P .

We consider an incomplete market model with one traded stock and two correlated Brownian motions W, f W . The Brownian motion W drives the stock price, whose volatility and Sharpe ratio are adapted to the filtration e F := ( e Ft)0≤t≤T generated by f W . We show that the projections of the minimal entropy and minimal martingale measures onto e FT are related by an Esscher transform involving th...

We study the exponential utility indifference valuation of a contingent claim H when asset prices are given by a general semimartingale S. Under mild assumptions on H and S, we prove that a no-arbitrage type condition is fulfilled if and only if H has a certain representation. In this case, the indifference value can be written in terms of processes from that representation, which is useful in ...

In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assu...

A well-studied topic in finance is fitting pricing models to available market information; this is the inverse of the option pricing problem. The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential Lévy processes are calibrated using regularized weighted least squares with re...

In [Riesner, M., 2006. Hedging life insurance contracts in a Lévy process financial market. Insurance Math. Econom. 38, 599–608] the (locally) risk-minimizing hedging strategy for unit-linked life insurance contracts is determined in an incomplete financial market driven by a Lévy process. The considered risky asset is not a martingale under the original measure and therefore, a change of measu...

We derive an infimum law and a first-passage-time fluctuation theorem for entropy production of stochastic processes at steady state. We show that the ratio between the probability densities of the first-passage time to produce Stot of entropy and of the first-passage time to produce −Stot of entropy equals etot, with k Boltzmann’s constant. This first-passage-time fluctuation relation is valid...