Wahrscheinlichkeitstheorie

Klenke, Achim

doi:10.1007/978-3-642-36018-3

Cited by 42 publications

(51 citation statements)

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“…. dΛs, see, e.g., [23,Example 1.56]. This coincides a.s. with the more complex integral de nition in [34,38], so we can apply their results on properties of the integral.…”

Section: A Class Of Strong Idt Subordinatorssupporting

confidence: 56%

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Bernhart

Mai²,

Scherer

2015

Dependence Modeling

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Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choice when modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

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“…. dΛs, see, e.g., [23,Example 1.56]. This coincides a.s. with the more complex integral de nition in [34,38], so we can apply their results on properties of the integral.…”

Section: A Class Of Strong Idt Subordinatorssupporting

confidence: 56%

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Bernhart

Mai²,

Scherer

2015

Dependence Modeling

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“…Because of

E [z (t)] = 0

, we have

E [d a] = 0

, i.e., the expected change of a is zero. Note that the process is nonnegative if

a (0) \geq 0

and that

a (t) = 0

for all future

t \geq t_{0}

a (t_{0}) = 0

(for details on the GBM and standard Brownian Motions, see Klenke, , Ch. 21 & 25; Øksendal, , pp.…”

Section: The Modelmentioning

confidence: 99%

A real options approach to amenity valuation: The role of uncertainty and risk aversion

Mense¹

2017

Journal of Regional Science

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Many empirical studies in the fields of urban and environmental economics rely on the hedonic pricing framework. This paper draws attention to two important elements that are not covered by this theory: uncertainty and relocation costs. It develops a theoretical model where agents face uncertainty, but may accumulate savings as a form of self‐insurance. It shows that uncertainty pushes up relocation costs due to the option value of waiting, while self‐insurance helps to reduce this lock‐in problem. Moreover, the model suggests that the implicit price of environmental quality increases with uncertainty even if agents are risk‐neutral.

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“…Clearly, if A ∈ A, we have B ⊂ D A . From Dynkins π-λ-Theorem (for details see Klenke [63,Satz 1.19]), it follows that σ(B) = δ(B) ⊂ D A . By the symmetry property of the conditional independence of two sets, this fact can be reformulated as A ⊂ D B for every B ∈ σ(B).…”

Section: Enlargements Of Filtrations and The Martingale Invariance Prmentioning

confidence: 99%

A multiple-curve Lévy forward rate model in a two-price economy

Eberlein

Gerhart

2017

Quantitative Finance

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Abstract. In this thesis, we combine and merge the multiple-curve approach and the two-price theory based on acceptability indices in a Lévy interest rate model.A multiple-curve Heath-Jarrow-Morton (HJM) forward rate model driven by time-inhomogeneous Lévy processes (a multiple-curve Lévy term structure model) is presented. We nd deterministic conditions which ensure the monotonicity of the curves. Explicit valuation formulas for some interest rate derivatives are established, namely forward rate agreements, swaps, caps, oors and digital options. These formulas can numerically be evaluated very fast by using the Fourier based valuation method. Furthermore, we apply the two-price theory to this multiple-curve setting. Ask and bid model prices of caplets, oorlets and digital options are derived.A general procedure how to calibrate this two-price multiple-curve interest rate model to market data is described. As a practical application, the model is calibrated to market prices of caps for dates before and after the global nancial crisis. CONTENTS

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Wahrscheinlichkeitstheorie

Cited by 42 publications

References 0 publications

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

A real options approach to amenity valuation: The role of uncertainty and risk aversion

A multiple-curve Lévy forward rate model in a two-price economy

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