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The Annals of Applied Probability, ISSN 1050-5164, 4/2015, Volume 25, Issue 2, pp. 823 - 859
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a... 
Fundamental Theorem of Asset Pricing | Nondominated model | Optional decomposition | Knightian uncertainty | Martingale measure | Superhedging | martingale measure | PRICES | FUNDAMENTAL THEOREM | optional decomposition | CONTINGENT CLAIMS | STATISTICS & PROBABILITY | superhedging | nondominated model | Probability | Mathematics | 93E20 | 49L20 | 60G42 | 91B28
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 2/2014, Volume 24, Issue 1, pp. 312 - 336
We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade... 
Call options | Investors | Arbitrage | Transportation | Ordinary differential equations | Financial securities | Mathematics | Stopping distances | Preprints | Martingales | Optimal control | Convex duality | Volatility uncertainty | MAXIMUM | CONTINGENT CLAIMS | STATISTICS & PROBABILITY | volatility uncertainty | OPTIMAL TRANSPORTATION | convex duality | 49L20 | 60J60 | 49L25 | 35K55
Journal Article
The Annals of Probability, ISSN 0091-1798, 3/2015, Volume 43, Issue 2, pp. 572 - 604
We introduce a new class of backward stochastic differential equations in which the T-terminal value YT of the solution (Y, Z) is not fixed as a random... 
Stochastic target | Backward stochastic differential equations | Optimal control | stochastic target | optimal control | STATISTICS & PROBABILITY | STOCHASTIC TARGET PROBLEMS | Probability | Mathematics | 60H10 | 93E20 | 49L20 | 91G80
Journal Article
Stochastic Models, ISSN 1532-6349, 10/2019, Volume 35, Issue 4, pp. 469 - 495
In this article, we consider an optimal execution problem with fixed time horizon and bounded transaction rate, which is more natural in practice. We show... 
Constrained price impact | 93E20 | 49L20 | stochastic bang-bang control | optimal order execution | 91G80
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 6/2014, Volume 24, Issue 3, pp. 899 - 934
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1456 - 1476
In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The “factoring” approach alleviates... 
Computational Mathematics and Numerical Analysis | 65N12 | Eikonal | Theoretical, Mathematical and Computational Physics | Factoring | Rarefaction fans | Mathematics | 49L20 | Algorithms | Mathematical and Computational Engineering | 49N90 | Robotic navigation | Fast Marching | 49L25 | 65N22 | MATHEMATICS, APPLIED
Journal Article
International Journal of Control, ISSN 0020-7179, 10/2019, Volume 92, Issue 10, pp. 2263 - 2273
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2018, Volume 56, Issue 2, pp. 1038 - 1057
We propose a general framework for studying the optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the... 
Bayesian filtering | Uncertainty | Optimal control | MATHEMATICS, APPLIED | optimal control | uncertainty | AUTOMATION & CONTROL SYSTEMS | Probability | Mathematics
Journal Article
Advances in Applied Probability, ISSN 0001-8678, 09/2015, Volume 47, Issue 3, pp. 652 - 667
The class of restless bandits as proposed by Whittle (1988) have long been known to be intractable. This paper presents an optimality result which extends that... 
49M20 | 90C40 | 49L20 | 93E20 | multi-action restless bandit | asymptotic optimality | Index heuristic | stochastic resource allocation
Journal Article
Journal of Applied Probability, ISSN 0021-9002, 09/2015, Volume 52, Issue 3, pp. 718 - 735
In a defaultable market, an investor trades having only partial information about the behavior of the market. Taking into account the intraday stock movements,... 
93E11 | Optimal investment | 49L20 | 93E03 | dynamic programming | default time | exponential utility | filtering | backward stochastic differential equation
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 5/2019, Volume 39, Issue 3, pp. 857 - 873
This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary... 
backward stochastic partial differential equation | viscosity solution | 49L20 | 93E20 | Analysis | Stochastic Hamilton-Jacobi equation | optimal stochastic control | Mathematics, general | 35D40 | Mathematics | 49L25 | 60H15
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 04/2017, Volume 127, Issue 4, pp. 1171 - 1203
We design an importance sampling scheme for backward stochastic differential equations (BSDEs) that minimizes the conditional variance occurring in... 
Backward stochastic differential equations | Empirical regressions | Importance sampling | 49L20 | 65C30 | 93E24 | 60H07 | 62Jxx | STATISTICS & PROBABILITY | VARIANCE | Analysis | Algorithms | Differential equations
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 2018, Volume 181, Issue 3, pp. 1076 - 1089
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2016, Volume 54, Issue 2, pp. 1017 - 1029
In this note, we propose two different approaches to rigorously justify a pseudo-Markov property for controlled diffusion processes which is often (explicitly... 
Dynamic programming principle | Stochastic control | Pseudo-Markov property | Martingale problem | Probability | Mathematics
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 3635 - 3647
In this paper, by using a recent fixed point theorem, we study the existence and uniqueness of positive solutions for the following m-point fractional boundary... 
m-point fractional boundary value problem | 47H10 | 49L20 | Fixed point theorem | Theoretical, Mathematical and Computational Physics | Positive solution | Mathematics, general | Mathematics | Applications of Mathematics
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2018, Volume 370, Issue 3, pp. 2115 - 2160
Journal Article
Dynamical Systems, ISSN 1468-9367, 10/2019, Volume 34, Issue 4, pp. 685 - 709
We study a skew product IFS on the cylinder defined by Baker-like maps associated to a finite family of potential functions and the doubling map. We show that... 
discounted ergodic averages | 37-XX | Bellman equation | 28Dxx | dynamic programming | 90C39 | ergodic theory | 37Hxx | 37L40 | ergodic optimization | SRB measures | Iterated function system | 49Lxx | 49L20 | 37B10 | 37B55 | MATHEMATICS, APPLIED | MATHER | MINIMIZING MEASURES | PHYSICS, MATHEMATICAL | PRINCIPLES | Maximization | Maps | Invariants | Optimization | Ergodic processes | Cylinders
Journal Article
ANNALS OF APPLIED PROBABILITY, ISSN 1050-5164, 02/2018, Volume 28, Issue 1, pp. 1 - 34
In this paper, we aim to develop the stochastic control theory of branching diffusion processes where both the movement and the reproduction of the particles... 
VISCOSITY SOLUTIONS | viscosity solution | dynamic programming principle | Hamilton-Jacobi-Bellman equation | branching diffusion process | CONSTRUCTION | Stochastic control | STATISTICS & PROBABILITY
Journal Article
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