Asset Pricing - Constrained by Past Consumption Decisions by Lars Grüne and Willi Semmler

The attempt to match asset price characteristics such as the risk-free interest rate, equity premium and the Sharpe ratio with data for models with instantaneous consumption decisions and time separable preferences has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation where past consumption acts as a constraint on current consumption. In those models, surplus consumption, consumption over and above past consumption, improves welfare, yet habit formation gives rise to an additional state variable. By studying such a model we also allow for adjustment costs of investment. The asset price characteristics that one obtains from those models may depend on the solution techniques employed. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the above mentioned asset price characteristics where past consumption decisions are treated as an additional state variable. Since, as shown in Grüne and Semmler (2004), our method produces only negligible errors it is suitable to be used as solution technique for such models with more complicated decision structure. Using our solution methods shows that there are still remaining puzzles for the consumption based asset pricing model. JEL Classification: C60, C61, C63, D90, G12