### Abstract

This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

Original language | English (US) |
---|---|

Pages (from-to) | 208-248 |

Number of pages | 41 |

Journal | Mathematical Finance |

Volume | 29 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- backward stochastic differential equations
- non-Markov control
- partial information
- portfolio optimization

### ASJC Scopus subject areas

- Accounting
- Finance
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Applied Mathematics

### Cite this

**Backward SDEs for control with partial information.** / Papanicolaou, Andrew.

Research output: Contribution to journal › Article

*Mathematical Finance*, vol. 29, no. 1, pp. 208-248. https://doi.org/10.1111/mafi.12174

}

TY - JOUR

T1 - Backward SDEs for control with partial information

AU - Papanicolaou, Andrew

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

AB - This paper considers a non-Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non-Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

KW - backward stochastic differential equations

KW - non-Markov control

KW - partial information

KW - portfolio optimization

UR - http://www.scopus.com/inward/record.url?scp=85054160581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054160581&partnerID=8YFLogxK

U2 - 10.1111/mafi.12174

DO - 10.1111/mafi.12174

M3 - Article

AN - SCOPUS:85054160581

VL - 29

SP - 208

EP - 248

JO - Mathematical Finance

JF - Mathematical Finance

SN - 0960-1627

IS - 1

ER -