Optimal investment with intermediate consumption under no unbounded profit with bounded risk

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal and dual value functions.Comment: 10 pages, revised version, to appear in the Applied Probability Journal

Power Utility Maximization in Constrained Exponential L\'evy Models

We study power utility maximization for exponential L\'evy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the L\'evy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences for q-optimal martingale measures are discussed as well as extensions to non-convex constraints.Comment: 22 pages; forthcoming in 'Mathematical Finance

Relative Extinction of Heterogeneous Agents

In all the existing literature on survival in heterogeneous economies, the rate at which an agent vanishes in the long run relative to another agent can be characterized by the difference of the so-called survival indices, where each survival index only depends on the preferences of the corresponding agent and the properties of the aggregate endowment. In particular, one agent experiences extinction relative to another (that is, the wealth ratio of the two agents goes to zero) if and only if she has a smaller survival index. We consider a simple complete market model and show that the survival index is more complex if there are more than two agents in the economy. In fact, the following phenomenon may take place: even if agent one experiences extinction relative to agent two, adding a third agent to the economy may reverse the situation and force the agent two to experience extinction relative to agent one. We also calculate the rates of convergence

Weak and strong no-arbitrage conditions for continuous financial markets

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for finan- cial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage opportunity (NA) and No Free Lunch with Vanishing Risk (NFLVR). We provide a complete characterization of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results