Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

A beta based framework for (lower) bond risk premia.

We use a no-arbitrage essentially affine three-factor model to estimate term premia in US and German ten-year government bond yields. In line with the existing literature, we find that estimated premia have followed a downward trend since the 1980s: from 4.9 per cent in 1981 to 0.7 per cent in 2006 for the US bond and from 3.3 to 0.5 per cent for the German one. Subsequently, using an Error Correction Model (ECM) we prove that the decline is explained by a decrease in global output variability and an increase in the power of ten-year government bonds to diversify the investors’ portfolios. In addition, the ECM also forecasts both the US and the German term premia converging to around one percentage point over a five year horizon. Long-term return expectations for ten-year government bonds will have to incorporate bond risk premia that - while in line with average excess returns during the twentieth century - are significantly lower than average excess returns over the last two decades.Term structure model, bond risk premium, modern portfolio theory

Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is to show that the risk-sensitive jump diffusion problem can be fully characterized in terms of a parabolic Hamilton-Jacobi-Bellman PDE rather than a PIDE, and that this PDE admits a classical C^{1,2} solution.Comment: 33 page

Liquidity, term spreads and monetary policy

We propose a model that delivers endogenous variations in term spreads driven primarily by banks' portfolio decision and their appetite to bear the risk of maturity transformation. We first show that fluctuations of the future profitability of banks' portfolios affect their ability to cover for any liquidity shortage and hence influence the premium they require to carry maturity risk. During a boom, profitability is increasing and thus spreads are low, while during a recession profitability is decreasing and spreads are high, in accordance with the cyclical properties of term spreads in the data. Second, we use the model to look at monetary policy and show that allowing banks to sell long-term assets to the central bank after a liquidity shock leads to a sharp decrease in long-term rates and term spreads. Such interventions have significant impact on long-term investment, decreasing the amplitude of output responses after a liquidity shock. The short-term rate does not need to be decreased as much and inflation turns out to be much higher than if no QE interventions were implemented. Finally, we provide macro and micro-econometric evidence for the U.S. confirming the importance of expected financial business profitability in the determination of term spread fluctuations