Pricing range notes within Wishart affine models

Chiarella, Carl; Fonseca, José Da; Grasselli, Martino

doi:10.1016/j.insmatheco.2014.07.008

Cited by 12 publications

(4 citation statements)

References 36 publications

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“…For a direct proof, see [18,Lemma 3.2]. 13 While the quoted material is stated within the framework of symmetric cones (Section 4), we only borrow the part that holds for general cones. 14 We mean elements of f ∈ C 2 b (V ), restricted to K. 15 The argument hinges on a density argument (see [16,Proof of Theorem B.3 ]), namely that the linear hull of fu(x), u ∈ (K * ) • , is dense in the space of rapidly decreasing functions S+ on K = S + d , the cone of d × d positive semi-definite matrices.…”

Section: Notesmentioning

confidence: 99%

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Geometric ergodicity of affine processes on cones

Mayerhofer

Stelzer

Vestweber

2020

Stochastic Processes and their Applications

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For affine processes on finite-dimensional cones, we give criteria for geometric ergodicitythat is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of the limiting distribution, where we exploit the crucial affine property, and finite moments, where we invoke the polynomial property of affine semigroups. Furthermore, we elaborate sufficient conditions for aperiodicity and irreducibility. Our results are applicable to Wishart processes with jumps on the positive semidefinite matrices, continuous-time branching processes with immigration in high dimensions, and classical termstructure models for credit and interest rate risk.

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Section: Notesmentioning

confidence: 99%

“…Wishart and general positive semi-definite affine models have also been successfully used to model interest rates (e.g. [8,13,41,45]). For stochastic processes the existence and uniqueness of stationary solutions as well as convergence to the stationary solution is of high interest.…”

mentioning

confidence: 99%

Geometric ergodicity of affine processes on cones

Mayerhofer

Stelzer

Vestweber

2020

Stochastic Processes and their Applications

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“…However for the sake of completeness, we also provide an Online Supporting Information as a quick reminder of its definition and basic properties. It has been successfully applied in both finance (Chiarella, DaFonseca, & Grasselli, 2014; Chiu & Wong, 2014; Gouriéroux, Jasiak, & Sufana, 2009) and life insurance (Cairns, Blake, & Dowd, 2006). In this paper, we show that Wishart distributions are also particularly useful in many nonlife insurance applications ranging from ratemaking to individual reserving.…”

Section: Wishart‐gamma Distribution For Multivariate Random Effectmentioning

confidence: 99%

Wishart‐gamma random effects models with applications to nonlife insurance

Denuit

2020

J of Risk & Insurance

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Random effects are particularly useful in insurance studies, to capture residual heterogeneity or to induce cross‐sectional and/or serial dependence, opening hence the door to many applications including experience rating and microreserving. However, their nonobservability often makes existing models computationally cumbersome in a multivariate context. In this paper, it is shown that the multivariate extension to the Gamma distribution based on Wishart distributions for random symmetric positive‐definite matrices (considering diagonal terms) is particularly tractable and convenient to model correlated random effects in multivariate frequency, severity and duration models. Three applications are discussed to demonstrate the versatility of the approach: (a) frequency‐based experience rating with several policies or guarantees per policyholder, (b) experience rating accounting for the correlation between claim frequency and severity components, and (c) joint modeling and forecasting of the time‐to‐payment and amount of payment in microlevel reserving, when both are subject to censoring.

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“…In particular, they provide natural models for the evolution of the covariance matrix of multi-asset prices that exhibit random dependence, for instance, the Wishart process [9], the jump-type Wishart process [34], and a certain class of matrix-valued Ornstein-Uhlenbeck processes driven by Lévy subordinators [7]. Among them, the Wishart process is the most popular one, and it has been successfully applied to generalize the well-known Heston model [24] to multi-asset setting, see also [3,8,10,15,19,20,21,22,23]. The jump-type Wishar process as introduced by Leippold and Trojani [34] allows jumps which help the model to fit better to real world interest rates or volatility of multi-asset prices.…”

Section: Introductionmentioning

confidence: 99%

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

Friesen¹,

Jin²,

Kremer³

et al. 2019

Preprint

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This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite d × d-matrices. In particular, for conservative and subcritical affine processes on this cone we show that a finite log-moment of the stateindependent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: firstly, in a specific metric induced by the Laplace transform and secondly, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.

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Pricing range notes within Wishart affine models

Cited by 12 publications

References 36 publications

Geometric ergodicity of affine processes on cones

Geometric ergodicity of affine processes on cones

Wishart‐gamma random effects models with applications to nonlife insurance

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

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