In the preceding chapter we showed that in a model with Gaussian diffusion factors the asset allocation problem reduces, via the change of measure technique, to a controlled diffusion problem in the factor process, even though there are jumps in the asset price model. The problem can be handled...

An important feature of the diffusion-based models presented in Part I is that they can be solved analytically, and as such do not require additional work to get the optimal investment strategy and the value function (aside from solving a Riccati equation and a linear ODE)…

The following sections are included:IntroductionFinancial Market, Investment Portfolio and BenchmarkDynamic Programming and the Value FunctionExistence of a Classical (C1,2) Solution Under Affine Drift AssumptionsExistence of a Classical (C1,2) Solution Under Standard Control AssumptionsFund...

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the...

This paper concerns the computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are correct. We draw the distinction between `external' and `internal' risk measures and concentrate on the latter, where we...

A model for large portfolio credit risk is developed by using results on the asymptotic behavior of stochastic networks. An efficient pricing technique is proposed using a newly-introduced quadrature algorithm. Accurate calibration to iTraxx tranche spreads is demonstrated.

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. The criterion, following earlier work by Bielecki, Pliska, Nagai...

An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market...

We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating...