On optimal investment for a behavioural investor in multiperiod incomplete market models

We provide easily verifiable conditions for the well-posedness of the optimal investment problem for a behavioral investor in an incomplete discrete-time multiperiod financial market model, for the first time in the literature. Under two different sets of assumptions we also establish the existence of optimal strategies

Pricing and Hedging Basis Risk under No Good Deal Assumption

We consider the problem of pricing and hedging an option written on a non-exchangeable asset when trading in a correlated asset is possible. This is a typical case of incomplete market where it is well known that the super-replication concept provides generally too high prices. Here, following J.H. Cochrane and J. Saá-Requejo, we study valuation under No Good Deal (NGD) Assumption. First, we clarify the notion of NGD for dynamic strategies, compute a lower and an upper bound and prove that in fact NGD price can be strictly higher that the one previously compute in the literature. We also propose a hedging strategy by imposing criterium on the variance of the replication's error. Finally, we provide various numerical illustrations showing the efficiency of NGD pricing and hedging.No Good Deal;basis risk;mean variance hedging

The robust superreplication problem: a dynamic approach

In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative to a family of probability measures $\mathcal{P}$. We first describe the evolution of $\pi_t(\xi)$ - the superhedging price at time $t$ of the liability $\xi$ at maturity $T$ - via a dynamic programming principle and show that $\pi_t(\xi)$ can be seen as a concave envelope of $\pi_{t+1}(\xi)$ evaluated at today's prices. Then we consider an optimal investment problem for a trader who is rolling over her robust superhedge and phrase this as a robust maximisation problem, where the expected utility of inter-temporal consumption is optimised subject to a robust superhedging constraint. This utility maximisation is carrried out under a new family of measures $\mathcal{P}^u$, which no longer have to capture regulatory or institutional risk views but rather represent trader's subjective views on market dynamics. Under suitable assumptions on the trader's utility functions, we show that optimal investment and consumption strategies exist and further specify when, and in what sense, these may be unique

Non-concave utility maximisation on the positive real axis in discrete time

We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.Comment: 20 page

No free lunch for markets with multiple num\'eraires

We consider a global market constituted by several submarkets, each with its own assets and num\'eraire. We provide theoretical foundations for the existence of equivalent martingale measures and results on superreplication prices which allows to take into account difference of features between submarkets

Risk-neutral pricing for Arbitrage Pricing Theory

We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the superreplication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their risk-aversion tends to infinity