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A stochastic overlapping generation model with a continuum of agents

Emmanuelle Augeraud-Véron, Delphine David (2008)

Banach Center Publications

We consider a stochastic overlapping generations model for a continuum of individuals with finite lives in presence of a financial market. In this paper, an agent's heterogeneity is given by the dates of birth of the household members, in contrast to standard models, in which each agent has his own aversion coefficient on his utility function. By means of martingale arguments, we compute the agent's optimal consumption and portfolio. A characterization of interest rate trajectories is given by mixed-type...

An Approach to Wealth Modelling

Stoynov, Pavel (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 60G48, 60G20, 60G15, 60G17. JEL Classification: G10The change in the wealth of a market agent (an investor, a company, a bank etc.) in an economy is a popular topic in finance. In this paper, we propose a general stochastic model describing the wealth process and give some of its properties and special cases. A result regarding the probability of default within the framework of the model is also offered.

An equilibrium model for electricity auctions

Juri Hinz (2003)

Applicationes Mathematicae

This work discusses the process of price formation for electrical energy within an auction-like trading environment. Calculating optimal bid strategies of power producers by equilibrium arguments, we obtain the corresponding electricity price and estimate its tail behavior.

Constrained portfolio liquidation in a limit order book model

Aurélien Alfonsi, Antje Fruth, Alexander Schied (2008)

Banach Center Publications

We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Obizhaeva and Wang (2006). We extend their model by allowing for a time-dependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. Our main results...

Dependent defaults and credit migrations

Tomasz R. Bielecki, Marek Rutkowski (2003)

Applicationes Mathematicae

The paper deals with the modelling of mutually dependent default times of several credit names through the intensity-based approach. We extend to the case of multiple ratings some previous results due to Schmidt (1998), Kusuoka (1999) and Jarrow and Yu (2001). The issue of the arbitrage valuation of simple basket credit derivatives is also briefly examined. We argue that our approach leads, in some cases, to a significant reduction of the dimensionality of the valuation problem at hand.

Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching

Paul Gassiat, Fausto Gozzi, Huyên Pham (2015)

Banach Center Publications

We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption...

Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization

Soňa Kilianová, Daniel Ševčovič (2018)


In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ( C V a R D ) based Sharpe ratio for measuring...

Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model

Kurt L. Helmes, Torsten Templin (2015)

Banach Center Publications

We analyze the optimal sales process of a stochastic advertising and pricing model with constant demand elasticities. We derive explicit formulae of the densities of the (optimal) sales times and (optimal) prices when a fixed finite number of units of a product are to be sold during a finite sales period or an infinite one. Furthermore, for any time t the exact distribution of the inventory, i.e. the number of unsold items, at t is determined and will be expressed in terms of elementary functions....

Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games

César U. S. Solis, Julio B. Clempner, Alexander S. Poznyak (2019)


This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves defenders and...

Incompleteness of the bond market with Lévy noise under the physical measure

Michał Barski (2015)

Banach Center Publications

The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.

Integral representations of risk functions for basket derivatives

Michał Barski (2012)

Applicationes Mathematicae

The risk minimizing problem E [ l ( ( H - X T x , π ) ) ] π m i n in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for l(x) = x and l ( x ) = x p , with p > 1 for digital, quantos, outperformance and spread options are derived.

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