Stochastic Control of Corporate Investment when Output Affects Future Prices

Investment Frictions and Leverage Dynamics

“…Therefore, numerical solutions are reformulated into finite horizon approximation. 35 I initialize the procedure by approximating (guessing) values in each node of the terminal 35 See Kushner and Dupuis (1992), Barraquand and Martineau (1995) and Langetieg (1986) for the theory and applications numerical of methods of stochastic control problems. Flam and Wets (1987) and Mercenier and Michel (1994) discuss the approximation of infinite horizon problems in the deterministic dynamic programming models.…”

Market Imperfections, Investment Optionality and Default Spreads

“…Note that default probabilities generated directly from our model are calculated under the risk neutral measure, which makes them difficult to interpret. 23 To calculate the default probabilities under the real measure we choose the drift of the long-term lease level to match the observed capital returns for office buildings. From the NCREIF subindex for office buildings, the average capital return is 4% per year, which can be roughly matched in our model by choosing a real drift for the long term lease level of 3%.…”

“…They argue that the actual cumulative default rate is even higher, perhaps up to 30%, since some loans in the pool were not counted as in default because they were either sold 23 To compute the default probabilities under the real measure we first determine the default boundary, as described in Appendix A.2. We then adjust the drift of the long-term lease rate level so that capital returns generated by the model match observed ones, and compute the probability that the adjusted stochastic process will reach the default boundary.…”

“…31 In each node on the grid (r, l, L, M ) the partial derivatives are approximated using first differences. 32 The values of the all-equity project at each node of the terminal approximation time are set to the values of the expected cash flows assuming that the quality level is kept 29 See, for example, Kushner and Dupuis (1992) [22], Barraquand and Martineau (1995) [3] and Langetieg (1986) [23] for the theory of numerical methods for stochastic control problems. 30 Flam and Wets (1987) [13] and Mercenier and Michel (1994) [32] also discuss the approximation of infinite horizon problems in deterministic dynamic programming models.…”

Market Imperfections, Investment Flexibility, and Default Spreads

“…37 37 See, for example, Kushner and Dupuis (2001), Barraquand and Martineau (1995) and Langetieg (1986) for the theory of numerical methods for stochastic control problems. …”