We develop a method that allows one to compute incomplete-market equilibria routinely for Markovian equilibria (when they exist). The main difficulty to be overcome arises from the set of state variables. There are, of course, exogenous state variables driving the economy but, in an incomplete...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a...

We study capital requirements for bounded financial positions defined as the minimum amount of capital to invest in a chosen eligible asset targeting a pre-specified acceptability test. We allow for general acceptance sets and general eligible assets, including defaultable bonds. Since the...

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the...

The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of in...

We study mean-variance hedging under portfolio constraints in a general semimartingale model. The constraints are formulated via predictable correspondences, meaning that the trading strategy is restricted to lie in a closed convex set which may depend on the state and time in a predictable way....

We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterise its three coefficient processes as solutions of...

An equivalent sigma-martingale measure (EsigmaMM) for a given stochastic process S is a probability measure R equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an EsigmaMM is equivalent to a classical absence-of-arbitrage property of S, and is invariant if...

We introduce a novel semi-parametric estimator of the price of American options in a discrete time, Markovian framework. The estimator is based on a parametric specification of the stochasticdiscount factor and is non-parametric w.r.t. the historical dynamics of the state variables. The...