Moderate deviations for sums of dependent claims in a size-dependent renewal risk model

Fu, Ke-Ang; Shen, Xinmei

doi:10.1080/03610926.2015.1060338

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…For references to some other classical moderate deviations results (on empirical measures); e.g., see sections 6.7 and 7.4 of Dembo and Zeitouni (1998). Several authors have investigated moderate deviations in actuarial risk theory; see, e.g., Fu and Shen (2017) and references therein. The rest of the paper is organized as follows.…”

Section: (Ii)mentioning

confidence: 99%

Option pricing in the moderate deviations regime

Friz

Gerhold

Pinter

2017

Mathematical Finance

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We consider call option prices close to expiry in diffusion models, in an asymptotic regime (“moderately out of the money”) that interpolates between the well‐studied cases of at‐the‐money and out‐of‐the‐money regimes. First and higher order small‐time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.

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Section: (Ii)mentioning

confidence: 99%

Option pricing in the moderate deviations regime

Friz

Gerhold

Pinter

2017

Mathematical Finance

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“…Fu and Shen [ 6 ] proved the following key lemma when they considered moderate deviations for sums of claims in a size-dependent renewal risk model.…”

Section: Main Results and Discussionmentioning

confidence: 99%

“…It is natural to ask whether ( 3.3 ) can still hold for with as , and if it can, what conditions are appropriate. Similar problems were partly studied by Shen and Zhang [ 26 ] for a risk model based on the customer-arrival process, by Gao [ 7 ] and Liu [ 19 ] for the standard renewal risk model with independent and dependent claims, respectively and by Fu and Shen [ 6 ] for the sums of consistently varying tailed claims in a size-dependent renewal risk model.…”

Section: Applications In Insurancementioning

confidence: 99%