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The purpose of this paper is to highlight some of the key elements of the HJM approach as originally introduced in the framework of fixed income market models, to explain how the very same philosophy was implemented in the case of credit portfolio derivatives and to show how it can be extended to and used in the case of equity market models. In each case we show how the HJM approach naturally yields a consistency condition and a no-arbitrage condition in the spirit of the original work of Heath, Jarrow and Morton. Even though the actual computations and the derivation of the drift condition in the case of equity models seems to be new, the paper is intended as a survey of existing results, and as such, it is mostly pedagogical in nature.

We aim to construct a general framework for portfolio management in continuous time, encompassing both stocks and bonds. In these lecture notes we give an overview of the state of the art of optimal bond portfolios and we re-visit main results and mathematical constructions introduced in our previous publications (Ann. Appl. Probab. 15, 1260–1305 (2005) and Fin. Stoch. 9, 429–452 (2005)).

In these lecture notes we review through simple examples recent results on models for insider trading based on the theory of enlargement of filtrations and on anticipating calculus. In particular, we concentrate on the case of strong type of insiders. That is, insiders that have additional information in the a.s. sense. We explain how to treat the utility maximization problem for insiders in order to obtain models where the utility is finite. In the anticipating framework, we introduce models where the signal of the insider can not be revealed to the small trader even though the insider has an effect on the price (large trader effect).

This is the first paper in a series devoted to a tentative model for the influence of hedging on the dynamics of an asset. We study here the case of a “large” investor and solve two problems in the context of such a model: the question of the fair value (or liquidation value) of a “large” position and the question of pricing or hedging an option. In order to do so, we use a utility maximization approach and some new results in stochastic control theory.

In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer’s theorem and give en extension to an insurance model with investment in stock market. We then describe how large deviation approximation and importance sampling are used in rare event simulation for option pricing. We finally focus on large deviations methods in risk management for the estimation of large portfolio losses in credit risk and portfolio performance in market investment.