On Bergman completeness of non-hyperconvex domains

We study the problem of the boundary behaviour of the Bergman kernel and the Bergman completeness in some classes of bounded pseudoconvex domains, which contain also non-hyperconvex domains. Among the classes for which we prove the Bergman completeness and the convergence of the Bergman kernel to infinity while tending to the boundary are all bounded pseudoconvex balanced domains, all bounded Hartogs domains with balanced fibers over regular domains and some bounded Laurent-Hartogs domains.Comment: 13 page

Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation

Monte Carlo simulation methods have become more and more important in the financial sector in the past years. In this paper, we introduce a new simulation method for the estimation of the derivatives of prices of financial contracts with respect to (w.r.t.) certain distributional parameters called the ‘Greeks’. In particular, we assume that the underlying financial process is a Lévy-type process in discrete time. Our method is based on the Measure-Valued Differentiation (MVD) approach, which allows representation of derivatives as differences of two processes, called the phantoms. We discuss the applicability of MVD for different types of option pay-offs in combination with different types of models of the underlying and provide a framework for the applicability of MVD for path-dependent pay-off functions, as Lookback Options or Asian Options

Behavioral pricing of energy swing options by stochastic bilevel optimization

Holders of energy swing options are free to specify the amounts of energy to be delivered on short notice, paying a fixed price per unit delivered. Due to the complexity of potential demand patterns, risk elimination by replication of these contract at energy exchange markets is not possible. As a consequence, when selling delivery contracts, the energy producer has to explicitly consider the risk emanating from fluctuations in supply cost. The impact of these risk factors can be mitigated by the contract seller, who is an energy producer, to a certain extent: Supply cost fluctuations can be absorbed by the own generation portfolio whereas demand uncertainties can be influenced by the choice of the strike price, implicitly changing the buyer's behavior. Considering this, the determination of the optimal strike price can be formulated a a stochastic bilevel problem where the optimal decision of upper level player (price setting and production) depends on the optimal decision of a lower level player (demand depending on the price). We present a solution algorithm tailored to the resulting specific stochastic bilevel problem. We illstrate the effects of the behavioral pricing approach by studying behavioral price setting for natural gas swing options, highlighting in particulr the influence of the seller's production and contract portfolio as well as of the market liquidity on optimal exercise prices

Generalization of a theorem of Gonchar

Let $X, Y$ be two complex manifolds, let $D\subset X,$ $G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Under a geometric condition on the boundary sets $A$ and $B,$ we show that every function locally bounded, separately continuous on $W,$ continuous on $A\times B,$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a function continuous on a "domain of holomorphy" $\hat{W}$ and holomorphic on the interior of $\hat{W}.$Comment: 14 pages, to appear in Arkiv for Matemati

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

CVaR minimization by the SRA algorithm

Using the risk measure CV aR in �nancial analysis has become more and more popular recently. In this paper we apply CV aR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CV aR

Quantification of Loss of Access to Critical Services during Floods in Greater Jakarta: Integrating Social, Geospatial, and Network Perspectives

This work presents a framework for assessing the socio-physical disruption of critical infrastructure accessibility using the example of Greater Jakarta, a metropolitan area of the Indonesian city. The first pillar of the framework is damage quantification based on the real flood event in 2020. Within this pillar, the system network statistics before and shortly after the flood were compared. The results showed that the flood impeded access to facilities, distorted transport connectivity, and increased system vulnerability. Poverty was found to be negatively associated with surface elevation, suggesting that urbanization of flood-prone areas has occurred. The second pillar was a flood simulation. Our simulations identified the locations and clusters that are more vulnerable to the loss of access during floods, and the entire framework can be applied to other cities and urban areas globally and adapted to account for different disasters that physically affect urban infrastructure. This work demonstrated the feasibility of damage quantification and vulnerability assessment relying solely on open and publicly available data and tools. The framework, which uses satellite data on the occurrence of floods made available by space agencies in a timely manner, will allow for rapid ex post investigation of the socio-physical consequences of disasters. It will save resources, as the analysis can be performed by a single person, as opposed to expensive and time-consuming ground surveys. Ex ante vulnerability assessment based on simulations will help communities, urban planners, and emergency personnel better prepare for future shocks

Evolutionary multi-stage financial scenario tree generation

Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations (represented as scenario trees) have been suggested in the literature. In this paper, a new evolutionary algorithm to create scenario trees for multi-stage financial optimization models will be presented. Numerical results and implementation details conclude the paper