Related papers: Pricing multi-asset contingent claims in a multi-d…
In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the…
We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that…
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of…
Value adjustment of uncollateralized trades is determined within a risk-neutral pricing framework. When hedging such trades, investors cannot freely trade protection on their own name, thus facing an incomplete market. This fact is…
In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite…
This paper addresses an important gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution framework, with a particular focus on the Merton model. The…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
We reconsider the valuation of barrier options by means of binomial trees from a "forward looking" prospective rather than the more conventional "backward induction" one used by standard approaches. This reformulation allows us to write…
We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…
The paper summarizes key results of the benchmark approach with a focus on the concept of benchmark-neutral pricing. It applies these results to the pricing of an extreme-maturity European put option on a well-diversified stock index. The…
In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and…
In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian) an explicit second-order expansion formula for the power investor's value function -…
We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a…
Let $S^F$ be a $\mathbb{P}$-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on model coefficients which guarantee the completeness of the market in which in…
An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of…
We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of…
This paper studies the pricing of contingent claims of American style, using indifference pricing by fully dynamic convex risk measures. We provide a general definition of risk-indifference prices for buyers and sellers in continuous time,…
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…