On some Stochastic Control Problems arising in Environmental Economics and Commodity Markets

Koch T. On some Stochastic Control Problems arising in Environmental Economics and Commodity Markets. Bielefeld: Universität Bielefeld; 2020

Stochastic optimal control and regime switching : applications in economics

Economic decisions under uncertainty generally involve a change of stochastic regime. This thesis examines the formal conditions for optimizing such decisions and looks at applications to exchange rate intervention, physical investment and consumption behaviour. Many of these economic regime switchings can be mathematically formulated as stopping problems. Global optimality is achieved by applying Hamilton-Jacobi-Bellman equations in each regime, together with the joining conditions at the switching boundaries. Chapter 1 establishes the framework for optimisation and provides various boundary conditions for different switching cases. Chapter 2 applies optimal stopping techniques to derive optimal “time-consistent” exchange rate target zones in the presence of proportional/lump sum intervention costs. It further shows that such discretionary equilibria can be improved upon by a credible commitment to an exchange rate mechanism (such as ERM). Chapter 3 characterises the irreversible oil investment decision in the North Sea as an optimal regime switching problem. In the absence of Petroleum Revenue Tax (PRT), it shows how the optimal development decision will be deferred when real oil prices follow a geometric Brownian motion. In chapter 4, an intertemporal partial equilibrium model of investment is used to assess the effects of stochastic capital depreciation on optimal investment behaviour, in a context where a sales constraint effectively decomposes the problem into two distinct regimes. The presence of the uncertainty about depreciation reduces firm’s demand for investment; and increasing the variability of capital depreciation further reduces investment. The uncertainty also makes investment “smoother” than that under certainty. Finally, chapter 5 and 6 deal with optimal consumption/portfolio decisions in a two-asset model with shortselling and borrowing restrictions imposed. Chapter 5 formulates a regime switching problem due to the presence of the borrowing constraint and specifies the corresponding boundary conditions. Chapter 6 characterises optimal solutions to various combinations of parameters for constant relative and constant absolute risk aversion utility functions. In many cases, if labour income is fully diversifiable, the borrowing constraint only binds when the wealth level falls below a threshold, and risk taking behaviour at the low level of wealth is associated with a convex portion of the indirect utility function (value function). In such regime-switch cases, the introduction of the borrowing constraint makes consumption more volatile relative to income. It also generates the precautionary motive for saving

A functional Itô's calculus approach to convex risk measures with jump diffusion

Convex risk measures for European contingent claims are studied in a non-Markovian jump-diffusion modeling framework using functional Itô's calculus. Two representations for a convex risk measure are considered, one based on a nonlinear g-expectation and another one based on a representation theorem. Functional Itô's calculus for càdlàg processes, backward stochastic differential equations (BSDEs) with jumps and stochastic optimal control theory are used to discuss the evaluation of convex risk measures. FPDIEs and PDIEs for convex risk measures are derived in the Markovian and non-Markovian situations, respectively. An entropic risk measure, which is a particular case of a convex risk measure, is discussed.10 page(s

5 European & African Conference on Wind Engineering

The 5th European-African Conference of Wind Engineering is hosted in Florence, Tuscany, the city and the region where, in the early 15th century, pioneers moved the first steps, laying down the foundation stones of Mechanics and Applied Sciences (including fluid mechanics). These origins are well reflected by the astonishing visionary and revolutionary studies of Leonardo Da Vinci, whose kaleidoscopic genius intended the human being to become able to fly even 500 years ago… This is why the Organising Committee has decided to pay tribute to such a Genius by choosing Leonardo's "flying sphere" as the brand of 5th EACWE