In a discrete time setting, we study the central problem of giving a fair price to some financial
product. This problem has been mostly treated using martingale measures and no-arbitrage …

For several decades, the no-arbitrage (NA) condition and the martingale measures have
played a major role in the financial asset's pricing theory. We propose a new approach for …

How to compute (super) hedging costs in rather general financial market models with
transaction costs in discrete-time? Despite the huge literature on this topic, most of results …

In this paper, we consider the discrete-time setting, and the market model described by (S, F,
T) $. Herein F is the``public" flow of information which is available to all agents overtime, S is …

In this paper, a general framework is developed for continuous-time financial market models
defined from simple strategies through conditional topologies that avoid stochastic calculus …

This chapter gives a general formulation of convex stochastic optimization problems in finite
discrete time. The objective of the minimization problem is an integral functional given in …

This chapter studies the dynamic programming principle when applied to the general
stochastic optimization problem of Chap. 1. Our approach builds on the notion of conditional …

The usual theory of asset pricing in finance assumes that the financial strategies, ie the
quantity of risky assets to invest, are real-valued so that they are not integer-valued in …

In this paper, we introduce a large class of (so-called) conditional indicators, on a complete
probability space with respect to a sub σ-algebra. A conditional indicator is a positive …

We solve the problem of super-hedging European or Asian options for discrete-time
financial market models where executable prices are uncertain. The risky asset prices are …