Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Environmental changes and human activity threaten the fauna of many geographical areas. We exploit the entropy definition from thermodynamics to assess ecosystem stability. In particular, we study a minimal ecosystem on a lattice in which two species struggle for sur...

Convexity correction arises when one computes the expected value of an interest rate index under a probability measure other than its own natural martingale measure. As a typical example, the natural martingale measure of the swap rate is the swap measure with annuity as the numeraire. However, the evaluation of the discounted expectation of the payoff in a constant maturity swap (CMS) derivati...

In this paper we treat, under fairly general conditions, the question of whether asset prices admit a martingale measure when the markets are free of arbitrage opportunities. The arbitrage opportunities we consider are restricted to originate from simple trading strategies, which are most closely related to actual market portfolios. It is shown that if such simple arbitrage profits are excluded...

We give sufficient criteria for the Doléans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are sufficiently weak to be useful and verifiable, as illustrated by several non-trivial examples, without introducing artificial constraints. In particular, they make it possible to construct nonexplosive point processes...

1 Result and Discussion We consider a discrete-time infinite horizon model with an adapted d-dimensional process S = (S t) given on a stochastic basis (Ω, F, F = (F t) t=0,1,... , P). The notations used: M(P), M loc (P) and P are the sets of d-dimensional martingales, local martingales and predictable (i.e. (F t−1)-adapted) processes; H · S t = j≤t H j ∆S j. To our knowledge, this result was ne...

In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets, which we call Arbitrage de la classe S. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: for S = {Ω}, absence of Model...

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale ...

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale ...