Stochastic Finance

Föllmer, Hans; Schied, Alexander

doi:10.1515/9783110212075

Cited by 751 publications

(213 citation statements)

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“…For any X ∈ L 0 , agent i ∈ I is indifferent between the cash amount U i (X) and the corresponding risky position X; in other words, U i (X) is the certainty equivalent of X ∈ L 0 for agent i ∈ I . The functional −U i is an entropic risk measure in the terminology of convex risk measure literature; see, for example, [18,Chap. 4].…”

Section: Agents and Preferencesmentioning

confidence: 99%

Equilibrium in risk-sharing games

Anthropelos

Kardaras

2017

Finance Stoch

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The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. In this paper, we propose a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that agents' best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation, and it is proved to exist for an arbitrary number of agents and to be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different from their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk-tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium than compared to the Arrow-Debreu one. Keywords

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Section: Agents and Preferencesmentioning

confidence: 99%

Equilibrium in risk-sharing games

Anthropelos

Kardaras

2017

Finance Stoch

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“…A utility function that is particularly popular in insurance and financial mathematics (Goovaerts et al [32], Föllmer and Schied [27] and Mania and Schweizer [53]) and decision theory (Gollier [31]) is the exponential utility function. When u is exponential, we provide a solution to the portfolio choice and indifference valuation problems in the case that the penalty function c in (2.3) is an indicator function.…”

Section: Exponential Utility Under Multiple Priors Preferencesmentioning

confidence: 99%

“…27 We have that for every admissible π, U t (F + X (π) T ) = U g (π) t (F ) + X (π) t , where U g (π) (F ) is the unique solution to the BSDE with terminal condition F and driver function g (π) (t, z,z) = g (π) 1 (t, z) + R\{0} g (π) 2 (t, x,z(x))n p (t, dx) with g (π) 1 (t, z,z) := g 1 (t, z − π t σ t ) − π t b t and g (π) 2 (t, x,z(x)) := g 2 (t, x,z(x) − π t β t (x)).…”

mentioning

confidence: 99%

Robust Portfolio Choice and Indifference Valuation

Laeven

Stadje²

2014

Mathematics of OR

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We solve, theoretically and numerically, the problems of optimal portfolio choice and indifference valuation in a general continuous-time setting. The setting features (i) ambiguity and ambiguity averse preferences, (ii) discontinuities in the asset price processes, with a general and possibly infinite activity jump part next to a continuous diffusion part, and (iii) general and possibly non-convex trading constraints. We characterize our solutions as solutions to Backward Stochastic Differential Equations (BSDEs). We prove existence and uniqueness of the solution to the general class of BSDEs with jumps having a drift (or driver) that grows at most quadratically, encompassing the solutions to our portfolio choice and valuation problems as special cases. We provide an explicit decomposition of the excess return on an asset into a risk premium and an ambiguity premium, and a further decomposition into a piece stemming from the diffusion part and a piece stemming from the jump part. We further compute our solutions in a few examples by numerically solving the corresponding BSDEs using regression techniques.

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“…Q 1 , Q 2 coincide (see proof of Lemma 7.23 in [14]), implying E Q 1 e −rT ψ(S T ) = E Q 2 e −rT ψ(S T ) for a derivative ψ(S T ). Moreover, there exist axiomatizations for pricing rules in financial markets that guarantee the existence of martingale measures which are consistent with the observable call prices C(K) for all strikes K (cf.…”

Section: The Risk Neutral Valuation Principlementioning

confidence: 94%

“…reducing directly to a binomial model within out setting (cf. [14], Theorem 5.38). Hence arbitrage arguments alone are not sufficient for a justification of the risk neutral valuation.…”

Section: The Risk Neutral Valuation Principlementioning

confidence: 97%

Parametric Estimation of Risk Neutral Density Functions

Grith

Krätschmer

2011

Handbook of Computational Finance

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Summary. This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions determining the risk neutral distributions. We we shall differentiate between the direct and the indirect way. Following the direct way, parameter vectors are estimated which characterize the distributions from selected statistical families to model the risk neutral distributions. The idea of the indirect approach is to calibrate characteristic parameter vectors for stochastic models of the asset price processes, and then to extract the risk neutral density function via Fourier methods. For every of the reviewed methods the calculation of option prices under hypothetically true risk neutral distributions is a building block. We shall give explicit formula for call and put prices w.r.t. reviewed parametric statistical families used for direct estimation. Additionally, we shall introduce the Fast Fourier Transform method of call option pricing developed in [6]. It is intended to compare the reviewed estimation methods empirically.

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Stochastic Finance

Cited by 751 publications

References 0 publications

Equilibrium in risk-sharing games

Equilibrium in risk-sharing games

Robust Portfolio Choice and Indifference Valuation

Parametric Estimation of Risk Neutral Density Functions

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