Narrow Results

The paper offers a new perspective on optimal portfolio choice by investigating how and to what extent knowledge of an investor's desirable initial investment choice can be used to determine his future optimal portfolio allocations. Optimality of investment decisions is built on the so-called forward investment performance criteria and, in particular, on the time-monotone ones. It is shown that for this class of forward criteria the desired initial allocations completely characterize the future optimal investment strategies. The analysis uses the connection between a nonlinear equation, satisfied by the local risk tolerance, and the backward heat equation. Complete solutions are provided as well as various examples.

We reformulate the monetary policy model of Barro and Gordon (1983a) by using an extended game with observable delay where the hierarchy of play between the central bank and the private sector is endogenous. This allows us to endogenise the institutional setup wherein the monetary policy game takes place. We show that positive inflation may be observed due to mixed strategies rather than time inconsistency.

Cellini and Lambertini endogenize through a timing game the moves of the central bank and the private sector in a model of monetary policy la Barro and Gordon. They find a multiplicity of equilibria, as the two Stackelberg outcomes emerge as the solutions of the timing game, with different inflation levels. By using the risk-dominance criterion to select the equilibrium we prove that there is a discontinuity in the inflation bias, depending on the inflation aversion of the private sector.

This paper presents a solution formula for the payoff distribution procedure of a bargaining problem in cooperative differential game that would lead to a time consistent outcome. In particular, individual rationality is satisfied for every player throughout the cooperation period.

New approach to the definition of solution in cooperative differential games is considered. The approach is based on artificially truncated information about the game. It assumed that at each time, instant players have information about the structure of the game (payoff functions, motion equations) only for the next fixed time interval. Based on this information they make the decision. Looking Forward Approach is applied to the cases when the players are not sure about the dynamics of the game on the whole time interval $[0,T]$ and orient themselves on the game dynamics defined on the smaller time interval $\overline{T}$ ($0<\overline{T}<T$), on which they surely know that the game dynamics is not changing.

The study of dynamic coherent risk measures and risk adjusted values is intimately related to the study of Backward Stochastic Differential Equations. We will present some of these relations and will also present some links with quasi-linear PDE.

Longer horizon returns are constructed from data on daily returns. Observed drawbacks of a Lévy process are a sharp decrease in skewness and excess kurtosis. Drawbacks to scaling are a flat term structure of skewness and excess kurtosis. A strategy that combines some exposure to independent increments and some exposure to scaling is developed in the context of self decomposable daily return distributions. Estimations are conducted on 400 stocks and we report that a good strategy for constructing longer horizon returns can be that of accumulating as i.i.d. half the daily return while scaling the remainder at rate one half.

The paper offers a new perspective on optimal portfolio choice by investigating how and to what extent knowledge of an investor's desirable initial investment choice can be used to determine his future optimal portfolio allocations. Optimality of investment decisions is built on the so-called forward investment performance criteria and, in particular, on the time-monotone ones. It is shown that for this class of forward criteria the desired initial allocations completely characterize the future optimal investment strategies. The analysis uses the connection between a nonlinear equation, satisfied by the local risk tolerance, and the backward heat equation. Complete solutions are provided as well as various examples.