Discounting and Patience in Optimal Stopping and Control Problems

This paper establishes that the optimal stopping time of virtually any optimal stopping problem is increasing in "patience," understood as a particular partial order on discount rate functions. With Markov dynamics, the result holds in a continuation- domain sense even if stopping is combined with an optimal control problem. Under intuitive additional assumptions, we obtain comparative statics on both the optimal control and optimal stopping time for one-dimensional diusions. We provide a simple example where, without these assumptions, increased patience can precipitate stopping. We also show that, with optimal stopping and control, a project's expected value is decreasing in the interest rate, generalizing analogous results in a deterministic context. All our results are robust to the presence of a salvage value. As an application we show that the internal rate of return of any endogenously-interrupted project is essentially unique, even if the project also involves a management problem until its interruption. We also apply our results to the theory of optimal growth and capital deepening and to optimal bankruptcy decisions.capital growth, comparative statics, discounting, internal rate of return, optimal control, optimal stopping, patience, present value, project valuation

RANDOM PERTURBATIONS OF NON-SINGULAR TRANSFORMATIONS ON [0; 1]

We consider random perturbations of non-singular measur-\ud able transformations S on [0; 1]. By using the spectral decomposition\ud theorem of Komornik and Lasota, we prove that the existence of the\ud invariant densities for random perturbations of S. Moreover the densi-\ud ties for random perturbations with small noise strongly converges to the\ud deinsity for Perron-Frobenius operator corresponding to S with respect\ud to L1([0; 1])-norm

Development of reliability methodology for systems engineering. Volume III - Theoretical investigations - An approach to a class of reliability problems Final report

Random quantities from continuous time stochastic process with application to reliability and probabilit

Stochastic optimal growth with a non-compact state space

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [J. Econ. Theory 4 (1972)] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.

Differentiability of the value function in continuous-time economic models.

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous—time models of convex optimization arising in economics. We dispense with an interioiity condition which is quite restrictive in constrained optimization and it is usually hard to check in applications. The differentiability of the value function is used to prove Bellman's equation as well as the existence and continuity of the optimal feedback policy. We also establish uniqueness of the vector of dual variables under some conditions that rule out existence of asset pricing bubbles.Constrained optimization; Value function; Differentiability; Envelope theorem; Duality theory;

On Independence For Non-Additive Measures, With a Fubini Theorem

Recent models of decision making represent agents' beliefs by non-additive set-functions. An important technical question which arises in applications to diverse areas of economics is how to define independence of such set-functions. After arguing that the straightforward generalization of independence does not in general yield a unique product, in this work I show that, while Fubini's theorem is in general false if additivity is not granted, it is true when a certain type of function is being integrated. For these functions the iterated integrals coincide with the integral with respect to products which satisfy a certain property, strictly stronger than independence. I show that most of the assumptions made in these results are very close to being necessary. In general the mentioned property is still not strong enough to uniquely define a product. On the other hand I discuss some proposals which have been made in the literature, and I show that unicity can however be obtained when the product is assumed to be a belief function. Moreover I show that the unique product thus obtained has an intuitive justification when the marginals are distributions induced by random correspondences. Finally I use the results in the paper to discuss the question of randomization in decision models with non-additive beliefs

Differentiability of the Value Function in Continuous–Time Economic Models

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous-time models of convex optimization arising in economics. We dispense with an interiority condition which is quite restrictive in constrained optimization and it is usually hard to check in applications. The differentiability of the value function is used to prove Bellman’s equation as well as the existence and continuity of the optimal feedback policy. We also establish uniqueness of the vector of dual variables under some conditions that rule out existence of asset pricing bubbles.Constrained optimization, value function, differentiability, envelope therem, duality theory.

Robust designs for series estimation

We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a general perspective of constructing robust and e±cient designs for series estimators which is based on the integrated mean squared error criterion. A minimax approach is used to derive designs which are robust with respect to deviations caused by the bias and the possibility of heteroscedasticity. A special case results from the imposition of an unbiasedness constraint; the resulting unbiased designs are particularly simple, and easily implemented. Our results are illustrated by constructing robust designs for series estimation with spherical harmonic descriptors, Zernike polynomials and Chebyshev polynomials. --Chebyshev polynomials,direct estimation,minimax designs,robust designs,series estimation,spherical harmonic descriptors,unbiased design,Zernike polynomials