joint work with Rutger-Jan Lange, Kristian Støre
We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process; this can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone and linearly convergent sequence of lower bounds. In a case study, we demonstrate the effectiveness of POST by comparing it to the frequently used quasi-analytic method, showing some difficulties that arise when using the latter. POST has a clear convergence analysis, is straightforward to implement and robust in analysing multidimensional option-valuation problems of modest dimension.
joint work with Sjur Westgaard
We use a multistage stochastic programming model to study optimal hedging decisions for risk-averse salmon producers. The objective is to maximize the weighted sum of expected revenues from selling salmon either in the spot market or in futures contracts and Conditional Value-at-Risk (CVaR) of the revenues over the planning horizon. The scenario tree for the multistage model is generated based on a procedure that combines Principal Component Analysis and state space modelling. Results indicate that salmon producers should hedge price risk already at fairly low degrees of risk aversion.
joint work with Juan Vera, Onur Babat
Value-at-Risk (VaR) is one of the main regulatory tools used for risk management purposes. However, it is difficult to compute optimal VaR portfolios; that is, an optimal risk-reward portfolio allocation using VaR as the risk measure. This is due to VaR being non-convex and of combinatorial nature. Here, we present an algorithm to compute near-optimal VaR portfolios that takes advantage of a MILP formulation of the problem and provides a guarantee of the solution’s near-optimality.