69,963 research outputs found
Dynamic consistency for Stochastic Optimal Control problems
For a sequence of dynamic optimization problems, we aim at discussing a
notion of consistency over time. This notion can be informally introduced as
follows. At the very first time step , the decision maker formulates an
optimization problem that yields optimal decision rules for all the forthcoming
time step ; at the next time step , he is able to
formulate a new optimization problem starting at time that yields a new
sequence of optimal decision rules. This process can be continued until final
time is reached. A family of optimization problems formulated in this way
is said to be time consistent if the optimal strategies obtained when solving
the original problem remain optimal for all subsequent problems. The notion of
time consistency, well-known in the field of Economics, has been recently
introduced in the context of risk measures, notably by Artzner et al. (2007)
and studied in the Stochastic Programming framework by Shapiro (2009) and for
Markov Decision Processes (MDP) by Ruszczynski (2009). We here link this notion
with the concept of "state variable" in MDP, and show that a significant class
of dynamic optimization problems are dynamically consistent, provided that an
adequate state variable is chosen
Computing Markov-perfect optimal policies in business-cycle models
Time inconsistency is an essential feature of many policy problems. This paper presents and compares three methods for computing Markov-perfect optimal policies in stochastic nonlinear business cycle models. The methods considered include value function iteration, generalized Euler equations, and parameterized shadow prices. In the context of a business cycle model in which a fiscal authority chooses government spending and income taxation optimally, although lacking the ability to commit, we show that the solutions obtained using value function iteration and generalized Euler equations are somewhat more accurate than that obtained using parameterized shadow prices. Among these three methods, we show that value function iteration can be applied easily, even to environments that include a risk-sensitive fiscal authority and/or inequality constraints on government spending. We show that the risk-sensitive fiscal authority lowers government spending and income taxation, reducing the disincentive to accumulate wealth that households face
Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure
The discrete-time mean-variance portfolio selection formulation, a
representative of general dynamic mean-risk portfolio selection problems, does
not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated
pre-committed efficient policy may become inefficient when considering the
corresponding truncated problem, thus stimulating investors' irrational
investment behavior. We investigate analytically effects of portfolio
constraints on time consistency of efficiency for convex cone constrained
markets. More specifically, we derive the semi-analytical expressions for the
pre-committed efficient mean-variance policy and the minimum-variance signed
supermartingale measure (VSSM) and reveal their close relationship. Our
analysis shows that the pre-committed discrete-time efficient mean-variance
policy satisfies TCIE if and only if the conditional expectation of VSSM's
density (with respect to the original probability measure) is nonnegative, or
once the conditional expectation becomes negative, it remains at the same
negative value until the terminal time. Our findings indicate that the property
of time consistency in efficiency only depends on the basic market setting,
including portfolio constraints, and this fact motivates us to establish a
general solution framework in constructing TCIE dynamic portfolio selection
problem formulations by introducing suitable portfolio constraints
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Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
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