Pricing dynamic fund protection under hidden Markov models

Kun Fan; Yang Shen; Tak Kuen Siu; Rongming Wang

doi:10.1093/imaman/dpw014

Pricing dynamic fund protection under hidden Markov models

Kun Fan^*
, Yang Shen
, Tak Kuen Siu
, Rongming Wang

^*Corresponding author for this work

School of Statistics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this article, we discuss the pricing of dynamic fund protection when the value process of the investment fund is governed by a geometric Brownian motion with parameters modulated by a continuous-time, finitestate hidden Markov chain. Under a risk-neutral probability measure, selected by the Esscher transform, we adopt the partial differential equation approach to value the dynamic fund protection. Using the estimated sequence of the hidden Markov chain, we apply the Baum-Welch algorithm and the Viterbi algorithm to derive the maximum likelihood estimates of the parameters. Numerical examples are provided to illustrate the practical implementation of the model.

Original language	English
Pages (from-to)	99-117
Number of pages	19
Journal	IMA Journal of Management Mathematics
Volume	29
Issue number	1
DOIs	https://doi.org/10.1093/imaman/dpw014
State	Published - 1 Jan 2018

Keywords

Baum-Welch algorithm
Dynamic Fund protection
Viterbi algorithm
hidden Markov model

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10.1093/imaman/dpw014

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title = "Pricing dynamic fund protection under hidden Markov models",

abstract = "In this article, we discuss the pricing of dynamic fund protection when the value process of the investment fund is governed by a geometric Brownian motion with parameters modulated by a continuous-time, finitestate hidden Markov chain. Under a risk-neutral probability measure, selected by the Esscher transform, we adopt the partial differential equation approach to value the dynamic fund protection. Using the estimated sequence of the hidden Markov chain, we apply the Baum-Welch algorithm and the Viterbi algorithm to derive the maximum likelihood estimates of the parameters. Numerical examples are provided to illustrate the practical implementation of the model.",

keywords = "Baum-Welch algorithm, Dynamic Fund protection, Viterbi algorithm, hidden Markov model",

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T1 - Pricing dynamic fund protection under hidden Markov models

AU - Fan, Kun

AU - Shen, Yang

AU - Siu, Tak Kuen

AU - Wang, Rongming

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this article, we discuss the pricing of dynamic fund protection when the value process of the investment fund is governed by a geometric Brownian motion with parameters modulated by a continuous-time, finitestate hidden Markov chain. Under a risk-neutral probability measure, selected by the Esscher transform, we adopt the partial differential equation approach to value the dynamic fund protection. Using the estimated sequence of the hidden Markov chain, we apply the Baum-Welch algorithm and the Viterbi algorithm to derive the maximum likelihood estimates of the parameters. Numerical examples are provided to illustrate the practical implementation of the model.

AB - In this article, we discuss the pricing of dynamic fund protection when the value process of the investment fund is governed by a geometric Brownian motion with parameters modulated by a continuous-time, finitestate hidden Markov chain. Under a risk-neutral probability measure, selected by the Esscher transform, we adopt the partial differential equation approach to value the dynamic fund protection. Using the estimated sequence of the hidden Markov chain, we apply the Baum-Welch algorithm and the Viterbi algorithm to derive the maximum likelihood estimates of the parameters. Numerical examples are provided to illustrate the practical implementation of the model.

KW - Baum-Welch algorithm

KW - Dynamic Fund protection

KW - Viterbi algorithm

KW - hidden Markov model

UR - https://www.scopus.com/pages/publications/85040122784

U2 - 10.1093/imaman/dpw014

DO - 10.1093/imaman/dpw014

M3 - 文章

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SN - 1471-678X

VL - 29

SP - 99

EP - 117

JO - IMA Journal of Management Mathematics

JF - IMA Journal of Management Mathematics

IS - 1

ER -

Pricing dynamic fund protection under hidden Markov models

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Keywords

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