Dynamic equity portfolios can be generated by positive twice continuously differentiable functions of the ranked capitalization weights of an equity market. The return on such a portfolio relative to the market follows a stochastic differential equation that decomposes the relative return into...

We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic...

We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump Lévy processes as driving noise instead of Brownian motion like in the Black and Scholes...

We firstly consider an investor faced with the classical Merton problem of optimal investment in a log-Brownian asset and a fixed-interest bond, but constrained only to change portfolio (and, if relevant, consumption) choices at times which are a multiple of h. We show that the cost of this...

We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time horizon a fixed amount of assets in order to maximise a net expected profit functional,...

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case...

We consider the problem of optimal investment in a risky asset, and in derivatives written on the price process of this asset, when the underlying asset price process is a pure jump Lévy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and...

This paper represents a model for the financial valuation of a firm which has control on the dividend payment stream and its risk, as well as potential profit by choosing different business activities among those available to it. Furthermore the company invests its free reserve in an asset,...

We consider an optimal portfolio-consumption problem which incorporates the notions of durability and intertemporal substitution. The logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve Lévy processes as driving noise instead of the more...

We consider a large insurance company whose surplus (reserve) is modeled by a Brownian motion. The company invests its surplus in stock market assets which may or may not contain an element of risk. To minimize the insurance risk there is a possibility to reinsure a part or the whole insurance...