### Abstract

Original language | English |
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Title of host publication | Extraction of Quantifiable Information from Complex Systems |

Editors | T.J. Barth, M. Griebel, D.E. Keyes, R.M. Nieminen, D. Roose, T. Schlick |

Place of Publication | Cham |

Publisher | Springer International Publishing AG |

Pages | 1-23 |

ISBN (Print) | 9783319081588 |

DOIs | |

Publication status | Published - 30 Sep 2014 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 102 |

### Fingerprint

### Cite this

*Extraction of Quantifiable Information from Complex Systems*(pp. 1-23). [Chapter 1] (Lecture Notes in Computational Science and Engineering; Vol. 102). Cham: Springer International Publishing AG. https://doi.org/10.1007/978-3-319-08159-5_1

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*Extraction of Quantifiable Information from Complex Systems.*, Chapter 1, Lecture Notes in Computational Science and Engineering, vol. 102, Springer International Publishing AG, Cham, pp. 1-23. https://doi.org/10.1007/978-3-319-08159-5_1

**Solving stochastic dynamic programs by convex optimization and simulation.** / Belomestny, Denis; Bender, Christian; Dickmann, Fabian; Schweizer, Nikolaus.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

TY - CHAP

T1 - Solving stochastic dynamic programs by convex optimization and simulation

AU - Belomestny, Denis

AU - Bender, Christian

AU - Dickmann, Fabian

AU - Schweizer, Nikolaus

PY - 2014/9/30

Y1 - 2014/9/30

N2 - In this chapter we review some recent progress on Monte Carlo methods for a class of stochastic dynamic programming equations, which accommodates optimal stopping problems and time discretization schemes for backward stochastic differential equations with convex generators. We first provide a primal maximization problem and a dual minimization problem, based on which confidence intervals for the value of the dynamic program can be constructed by Monte Carlo simulation. For the computation of the lower confidence bounds we apply martingale basis functions within a least-squares Monte Carlo implementation. For the upper confidence bounds we suggest a multilevel simulation within a nested Monte Carlo approach and, alternatively, a generic sieve optimization approach with a variance penalty term.

AB - In this chapter we review some recent progress on Monte Carlo methods for a class of stochastic dynamic programming equations, which accommodates optimal stopping problems and time discretization schemes for backward stochastic differential equations with convex generators. We first provide a primal maximization problem and a dual minimization problem, based on which confidence intervals for the value of the dynamic program can be constructed by Monte Carlo simulation. For the computation of the lower confidence bounds we apply martingale basis functions within a least-squares Monte Carlo implementation. For the upper confidence bounds we suggest a multilevel simulation within a nested Monte Carlo approach and, alternatively, a generic sieve optimization approach with a variance penalty term.

U2 - 10.1007/978-3-319-08159-5_1

DO - 10.1007/978-3-319-08159-5_1

M3 - Chapter

SN - 9783319081588

T3 - Lecture Notes in Computational Science and Engineering

SP - 1

EP - 23

BT - Extraction of Quantifiable Information from Complex Systems

A2 - Barth, T.J.

A2 - Griebel, M.

A2 - Keyes, D.E.

A2 - Nieminen, R.M.

A2 - Roose, D.

A2 - Schlick, T.

PB - Springer International Publishing AG

CY - Cham

ER -