Kourosh Marjani Rasmussen

A hybrid Constraint Programming/Mixed Integer Programming framework for the preventive signaling maintenance crew scheduling problem

Abstract A railway signaling system is a complex and interdependent system which should ensure the safe operation of trains. We introduce and address a mixed integer optimisation model for the preventive signal maintenance crew scheduling problem in the Danish railway system. The problem contains many practical constraints, such as temporal dependencies between crew schedules, the splitting of tasks across multiple days, crew competency requirements and several other managerial constraints. We propose a novel hybrid framework using Constraint Programming to generate initial feasible solutions to feed as ‘warm start’ solutions to a Mixed Integer Programming solver for further improvement. We apply this hybrid framework to a section of the Danish rail network and benchmark our results against both direct application of a Mixed Integer Programming solver and modelling the problem as a Constraint Optimisation Problem. Whereas the current practice of using a general purpose Mixed Integer Programming solver is only able to solve instances over a two-week planning horizon, the hybrid framework generates good results for problem instances over an eight-week period. In addition, the use of a Mixed Integer Programming solver to improve the initial solutions generated by Constraint Programming is shown to be significantly superior to addressing the problem as a Constraint Optimisation Problem.

Optimal Mortgage Loan Diversification

Homebuyers in several countries may finance the purchase of their properties using different variants of either adjustable-rate mortgages (ARMs) or fixed-rate mortgages (FRMs). The variety and complexity of these loan products poses a risk management task for mortgage bank advisors to recommend the right mortgage loan strategy for the individual mortgagor; almost all mortgage banks advise their customers to take a single loan product. This argument is often justified by the fact that trade frictions make it unattractive to hold a portfolio of loans as a private home owner. Even with transaction costs, however, we show in this paper that most mortgagors with some degree of risk aversion benefit from holding a mortgage portfolio. To do so we develop a multistage Mean-Conditional Value at Risk (MCVaR) model to consider the risk of the mortgage payment frequency function explicitly using a coherent risk measure. In addition to the diversification benefits we also show that the multistage model produces superior results as compared to single period models and that the solutions are robust with regards to changes in uncertainty parameters in particular for risk averse mortgagors. Finally, we show how the model can be used to calculate fair premia for adjustable rate mortgages with interest rate guarantees (caps) which are becoming increasingly popular as a hybrid product between the existing ARM and FRM mortgages.

Financial Giffen Goods: Examples and Counterexamples

In the basic Markowitz and Merton models, a stocks weight in efficient portfolios goes up if its expected rate of return goes up. Put differently, there are no financial Giffen goods. By an example from mortgage choice we illustrate that for more complicated portfolio problems Giffen effects do occur.

Portfolio selection under supply chain predictability

We investigate whether the returns of some industry portfolios predict the returns of other industry portfolios. We find a strong lead-lag structure which is statistically and economically significant. These findings suggest that information diffuses only gradually across industries. Moreover, we show that this predictability can be exploited in a mean-variance optimization framework. The calculated out-of-sample portfolio returns are attractive under different return-risk measures, and they show positive risk-adjusted excess returns which are not explained by classical risk factors.

Supply Chain Predictability of Returns and Portfolio Selection

We investigate whether the returns of some industry portfolios predict the returns of other industry portfolios. We find a strong lead-lag structure which is statistically and economically significant. These findings suggest that information diffuses only gradually across industries. Moreover, we show that this predictability can be exploited in a mean-variance optimization framework. The calculated out-of-sample portfolio returns are attractive under different return-risk measures, and they show positive risk-adjusted

Portfolio Optimization of Commodity Futures with Seasonal Components and Higher Moments

We investigate the diversification benefits of combining commodities with a traditional equity portfolio, while considering higher order statistical moments and seasonality. The literature suggests that the in-sample diversification benefits of commodities in portfolio optimization are not preserved out-of-sample. We provide an extensive in-sample and out-of-sample analysis with ten commodities and a stock index using the classical tangency mean-variance model and the maximum Omega ratio model. We show that seasonality in commodity returns should be considered, and leads to significant excess return and increase in Sharpe ratio.

New Paradigm in Mortgage Loan Advice

The Danish mortgage market has undergone considerable changes during the last 15 years. New and more complex variations of loan products have been introduced. Nevertheless, mortgage loan advice has remained, by large, unchanged. This paper addresses a study where a number of new refinancing rules are constructed with the help of a stochastic optimization model and the data mining method, CART.

Well ARMed and FiRM: diversification of mortgage loans for homebuyers

Individual homebuyers today are offered a wide range of mortgage options for financing the purchase of a house. Usually, homebuyers are also granted an option to repay the mortgage loan and in some countries (such as Denmark) it is particularly efficient to do so as market conditions change or the homebuyer’s situation warrants it. While, traditionally, a single mortgage loan would serve borrower needs, today it appears that a portfolio of loans may satisfy the mortgage needs of the individual and their appetite for risk much better. In this paper we develop a model for the diversification of mortgage loans of a homebuyer and apply it to data from the Danish market. Even in the presence of mortgage origination costs, it is shown that most risk-averse homebuyers will do well to consider a diversified portfolio of both fixed- and adjustable-rate mortgages (FRM and ARM). This is particularly the case if one takes, unavoidably, a long-term perspective in financing the purchase of a home through a mortgage loan.