数理金融
Under expected utility the local index of absolute risk aversion has played a central role in many applications. Besides, its link with the "global" concepts of the risk and probability premia has reinforced its attractiveness. This paper…
The problem of hedging and pricing sequences of contingent claims in large financial markets is studied. Connection between asymptotic arbitrage and behavior of the $\alpha$~-~quantile price is shown. The large Black-Scholes model is…
In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of…
An interacting Black-Scholes model for option pricing, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f(t) dW/dt, accounting for market imperfections and prices…
Existence of solutions to the Heath-Jarrow-Morton equation of the bond market with linear volatility and general L\'evy random factor is studied. Conditions for existence and non-existence of solutions in the class of bounded fields are…
The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on $[0,+\infty)$. Sufficient conditions for local and global existence are obtained . For…
The problem of completeness of the forward rate based bond market model driven by a L\'evy process under the physical measure is examined. The incompleteness of market in the case when the L\'evy measure has a density function is shown. The…
The intensity of a default time is obtained by assuming that the default indicator process has an absolutely continuous compensator. Here we drop the assumption of absolute continuity with respect to the Lebesgue measure and only assume…
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…
The problem of existence of arbitrage free and monotone CDO term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates with the use of the…
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these…
In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…
We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The…
In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent…
The paper considers an investment timing problem appearing in real options theory. Present values from an investment project are modeled by general diffusion process. We prove necessary and sufficient conditions under which an optimal…
We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the…
We provide new exact Taylor's series with fixed coefficients and without the remainder. We demonstrate the usefulness of this contribution by using it to obtain very simple solutions to (non-linear) PDEs. We also apply the method to the…
The paper develops general, discrete, non-probabilistic market models and minmax price bounds leading to price intervals for European options. The approach provides the trajectory based analogue of martingale-like properties as well as a…
We propose an affine extension of the Linear Gaussian term structure Model (LGM) such that the instantaneous covariation of the factors is given by an affine process on semidefinite positive matrices. First, we set up the model and present…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…