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Parabolic variational inequalities with generalized reflecting directions

Eduard Rotenstein (2015)

Open Mathematics

We study, in a Hilbert framework, some abstract parabolic variational inequalities, governed by reflecting subgradients with multiplicative perturbation, of the following type: y´(t)+ Ay(t)+0.t Θ(t,y(t)) ∂φ(y(t))∋f(t,y(t)),y(0) = y0,t ∈[0,T] where A is a linear self-adjoint operator, ∂φ is the subdifferential operator of a proper lower semicontinuous convex function φ defined on a suitable Hilbert space, and Θ is the perturbing term which acts on the set of reflecting directions, destroying the...

Performance of hedging strategies in interval models

Berend Roorda, Jacob Engwerda, Johannes M. Schumacher (2005)

Kybernetika

For a proper assessment of risks associated with the trading of derivatives, the performance of hedging strategies should be evaluated not only in the context of the idealized model that has served as the basis of strategy development, but also in the context of other models. In this paper we consider the class of so-called interval models as a possible testing ground. In the context of such models the fair price of a derivative contract is not uniquely determined and we characterize the interval...

Portfolio optimization for pension plans under hybrid stochastic and local volatility

Sung-Jin Yang, Jeong-Hoon Kim, Min-Ku Lee (2015)

Applications of Mathematics

Based upon an observation that it is too restrictive to assume a definite correlation of the underlying asset price and its volatility, we use a hybrid model of the constant elasticity of variance and stochastic volatility to study a portfolio optimization problem for pension plans. By using asymptotic analysis, we derive a correction to the optimal strategy for the constant elasticity of variance model and subsequently the fine structure of the corrected optimal strategy is revealed. The result...

Pricing bonds and CDS in the model with rating migration induced by a Cox process

Jacek Jakubowski, Mariusz Niewęgłowski (2008)

Banach Center Publications

We investigate the properties of a rating migration process assuming that it is given by subordination of a discrete time Markov chain and a Cox process. The problem of pricing of defaultable bonds with fractional recovery of par value with rating migration and credit default swaps is considered. As an example of applications of our results, we give an explicit solution to the pricing problem in a model with short rate and intensity processes given by the solution of a two-dimensional Ornstein-Uhlenbeck...

Principal-agent approach to environmental improvements policies

Wojciech Szatzschneider, Teresa Kwiatkowska (2010)

Banach Center Publications

Successful solution to any environmental problem implies working with Knightian uncertainty that explicitly deals with decision making under conditions of unstructured randomness. A 'wild' type of randomness that we will never discern due to its unstable properties makes the assignment of corresponding probabilities impossible. For that reason, the consideration of general economical factors within cost/benefit analysis must fail. So, instead of governmental intervention and a cup and trade scheme,...

Probabilistic methods for semilinear partial differential equations. Applications to finance

Dan Crisan, Konstantinos Manolarakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

With the pioneering work of [Pardoux and Peng, Syst. Contr. Lett.14 (1990) 55–61; Pardoux and Peng, Lecture Notes in Control and Information Sciences176 (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called backward stochastic differential equations. These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance....

Probabilistic properties of the continuous double auction

Martin Šmíd (2012)

Kybernetika

In this paper we formulate a general model of the continuous double auction. We (recursively) describe the distribution of the model. As a useful by-product, we give a (recursive) analytic description of the distribution of the process of the best quotes (bid and ask).

Producing the tangency portfolio as a corner portfolio

Reza Keykhaei, Mohamad-Taghi Jahandideh (2013)

RAIRO - Operations Research - Recherche Opérationnelle

One-fund theorem states that an efficient portfolio in a Mean-Variance (M-V) portfolio selection problem for a set of some risky assets and a riskless asset can be represented by a combination of a unique risky fund (tangency portfolio) and the riskless asset. In this paper, we introduce a method for which the tangency portfolio can be produced as a corner portfolio. So, the tangency portfolio can be computed easily and fast by any algorithm designed for tracing out the M-V efficient frontier via...

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