Search results for "Dynamic programming"
showing 10 items of 61 documents
Scenario modeling for the management of international bond portfolios
1998
We address the problem of portfolio management in the international bond markets. Interest rate risk in the local market, exchange rate volatility across markets, and decisions for hedging currency risk are integral parts of this problem. The paper develops a stochastic programming optimization model for integrating these decisions in a common framework. Monte Carlo simulation procedures, calibrated using historical observations of volatility and correlation data, generate jointly scenarios of interest and exchange rates. The decision maker's risk tolerance is incorporated through a utility function, and additional views on market outlook can also be incorporated in the form of user specifi…
A mate to die for? A model of conditional monogyny in cannibalistic spiders
2012
Monogynous males in various species actively limit themselves to mating with a single female in their lifetime. Whereas previous models have considered monogyny as an obligate mating strategy, here we explore the potential of monogyny to evolve as a context-specific (conditional) behavior. Using a state-dependent dynamic game model based on the biology of the cannibalistic spider Argiope bruennichi, we confirm that conditional monogyny can evolve under broad conditions, including an even sex ratio. We predict that males should make a terminal investment when mating with large, virgin females, especially if population density is low and the encounter occurs late in the season. We encourage e…
Asymptotic Hölder regularity for the ellipsoid process
2020
We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.
Convergence of dynamic programming principles for the $p$-Laplacian
2018
We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.
An evolutionary perspective on stress responses, damage and repair
2022
Variation in stress responses has been investigated in relation to environmental factors, species ecology, life history and fitness. Moreover, mechanistic studies have unravelled molecular mechanisms of how acute and chronic stress responses cause physiological impacts (‘damage’), and how this damage can be repaired. However, it is not yet understood how the fitness effects of damage and repair influence stress response evolution. Here we study the evolution of hormone levels as a function of stressor occurrence, damage and the efficiency of repair. We hypothesise that the evolution of stress responses depends on the fitness consequences of damage and the ability to repair that damage. To o…
CUDA-BLASTP: Accelerating BLASTP on CUDA-enabled graphics hardware
2011
Scanning protein sequence database is an often repeated task in computational biology and bioinformatics. However, scanning large protein databases, such as GenBank, with popular tools such as BLASTP requires long runtimes on sequential architectures. Due to the continuing rapid growth of sequence databases, there is a high demand to accelerate this task. In this paper, we demonstrate how GPUs, powered by the Compute Unified Device Architecture (CUDA), can be used as an efficient computational platform to accelerate the BLASTP algorithm. In order to exploit the GPU's capabilities for accelerating BLASTP, we have used a compressed deterministic finite state automaton for hit detection as wel…
Local regularity estimates for general discrete dynamic programming equations
2022
We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete extremal operators. Thus the results cover a quite general class of equations.
Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
2018
We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.
Hölder regularity for stochastic processes with bounded and measurable increments
2022
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…