General smoothing formulas for Markov-modulated Poisson observations

Elliott, Robert J.; Malcolm, W.P.

doi:10.1109/tac.2005.852565

Cited by 22 publications

(24 citation statements)

References 29 publications

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“…Now, let us move to the filtering equation for X . We follow the arguments of derivation given in Elliott and Malcolm (2005), Cohen and Elliott (2013). Firstly, we want to derive the unnormalized filter of X :…”

Section: Remarkmentioning

confidence: 99%

Optimal hedging for fund and insurance managers with partially observable investment flows

Fujii

Takahashi

2014

Quantitative Finance

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All financial practitioners are working in incomplete markets full of unhedgeable risk factors. Making the situation worse, they are only equipped with imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for sudden and possibly contagious changes in the investment flows from their clients so that they can avoid the over-as well as under-hedging. In this work, the prices of securities, the occurrences of insured events and (possibly a network of) investment flows are used to infer their drifts and intensities by a stochastic filtering technique. We utilize the inferred information to provide the optimal hedging strategy based on the mean-variance (or quadratic) risk criterion. A BSDE approach allows a systematic derivation of the optimal strategy, which is shown to be implementable by a set of simple ODEs and standard Monte Carlo simulation. The presented framework may also be useful for manufacturers and energy firms to install an efficient overlay of dynamic hedging by financial derivatives to minimize the costs.

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Section: Remarkmentioning

confidence: 99%

Optimal hedging for fund and insurance managers with partially observable investment flows

Fujii

Takahashi

2014

Quantitative Finance

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“…If one allows (λ A , λ D ) to depend explicitly on (κ, e, g), based on some empirical analysis for example, one can use the information of V (t, w) to achieve desirable intensities of investment flows. 7 The optimal hedging for an insurance portfolio…”

Section: )mentioning

confidence: 99%

Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows

Fujii

Takahashi

2014

SSRN Journal

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All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for sudden and possibly contagious changes in the investment flows from their clients so that they can avoid the over-as well as under-hedging. In this work, the prices of securities, the occurrences of insured events and (possibly a network of) the investment flows are used to infer their drifts and intensities by a stochastic filtering technique. We utilize the inferred information to provide the optimal hedging strategy based on the mean-variance (or quadratic) risk criterion. A BSDE approach allows a systematic derivation of the optimal strategy, which is shown to be implementable by a set of simple ODEs and the standard Monte Carlo simulation. The presented framework may also be useful for manufactures and energy firms to install an efficient overlay of dynamic hedging by financial derivatives to minimize the costs.

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“…There exist state smoothers for MMPP such as those given by Elliott and Malcolm (2005). Much the same as in the context of discrete-time hidden Markov models, a computationally efficient algorithm, fixed point smoothing algorithm, is available to estimate the probability of the underlying Markov chain in a given state at a specific time conditioned on all available observations, which only involves the forward and backward probabilities (see MacDonald and Zucchini (1997, pp …”

Section: Statistical Inference On the State Process And Observed Poinmentioning

confidence: 99%

Markov modulated Poisson process associated with state-dependent marks and its applications to the deep earthquakes

Shaochuan

2010

Ann Inst Stat Math

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In this paper, we introduce one type of Markov-Modulated Poisson Process (MMPP) whose arrival times are associated with state-dependent marks. Statistical inference problems including the derivation of the likelihood, parameter estimation through EM algorithm and statistical inference on the state process and the observed point process are addressed. A goodness-of-fit test is proposed for MMPP with statedependent marks by utilizing the theories of rescaling marked point process. We also perform some numerical simulations to indicate the effects of different marks on the efficiencies and accuracies of MLE. The effects of the attached marks on the estimation tend to be weakened for increasing data sizes. Then we apply these methods to characterize the occurrence patterns of New Zealand deep earthquakes through a second-order MMPP with state-dependent marks. In this model, the occurrence times and magnitudes of the deep earthquakes are associated with two levels of seismicity which evolves in terms of an unobservable two-state Markov chain.

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General smoothing formulas for Markov-modulated Poisson observations

Cited by 22 publications

References 29 publications

Optimal hedging for fund and insurance managers with partially observable investment flows

Optimal hedging for fund and insurance managers with partially observable investment flows

Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows

Markov modulated Poisson process associated with state-dependent marks and its applications to the deep earthquakes

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