2,656 research outputs found
The Wishart short rate model
We consider a short rate model, driven by a stochastic process on the cone of
positive semidefinite matrices. We derive sufficient conditions ensuring that
the model replicates normal, inverse or humped yield curves
Optimal control of predictive mean-field equations and applications to finance
We study a coupled system of controlled stochastic differential equations
(SDEs) driven by a Brownian motion and a compensated Poisson random measure,
consisting of a forward SDE in the unknown process and a
\emph{predictive mean-field} backward SDE (BSDE) in the unknowns . The driver of the BSDE at time may depend not just upon the
unknown processes , but also on the predicted future
value , defined by the conditional expectation . \\ We give a sufficient and a necessary
maximum principle for the optimal control of such systems, and then we apply
these results to the following two problems:\\ (i) Optimal portfolio in a
financial market with an \emph{insider influenced asset price process.} \\ (ii)
Optimal consumption rate from a cash flow modeled as a geometric It\^ o-L\'
evy SDE, with respect to \emph{predictive recursive utility}
Holomorphic transforms with application to affine processes
In a rather general setting of It\^o-L\'evy processes we study a class of
transforms (Fourier for example) of the state variable of a process which are
holomorphic in some disc around time zero in the complex plane. We show that
such transforms are related to a system of analytic vectors for the generator
of the process, and we state conditions which allow for holomorphic extension
of these transforms into a strip which contains the positive real axis. Based
on these extensions we develop a functional series expansion of these
transforms in terms of the constituents of the generator. As application, we
show that for multidimensional affine It\^o-L\'evy processes with state
dependent jump part the Fourier transform is holomorphic in a time strip under
some stationarity conditions, and give log-affine series representations for
the transform.Comment: 30 page
Cladding strategies for building-integrated photovoltaics
Photovoltaic cladding on the surfaces of commercial buildings has the potential for considerable reductions in carbon emissions due to embedded renewable power generation displacing conventional power utilization. In this paper, a model is described for the optimization of photovoltaic cladding densities on commercial building surfaces. The model uses a modified form of the ‘fill factor’ method for photovoltaic power supply coupled to new regression-based procedures for power demand estimation. An optimization is included based on a defined ‘mean index of satisfaction’ for matched power supply and demand (i.e., zero power exportation to the grid). The mean index of satisfaction directly translates to the reduction in carbon emission that might be expected over conventional power use. On clear days throughout the year, reductions of conventional power use of at least 60% can be achieved with an optimum cladding pattern targeted to lighting and small power load demands
Smart cable for design of high density metallic cross connect systems
The present invention to provide a smart cable system for high density metallic cross connect systems. In particular, this invention relates to the physical structure of cables and associated hardware needed to form the smart cable system for interconnecting cards in shelves and racks of high density metallic cross connect switching systems. This invention provides the cable installer the ability to connect cables to cards with minimal errors by using visual indicators. The visual indicators guide the cable installer such that he/she can properly install the cables into the appropriate connectors. The present invention also provides a means for detecting when and where the cables are connected within the cross connect system
Scope for Credit Risk Diversification
This paper considers a simple model of credit risk and derives the limit distribution of losses under different assumptions regarding the structure of systematic risk and the nature of exposure or firm heterogeneity. We derive fat-tailed correlated loss distributions arising from Gaussian risk factors and explore the potential for risk diversification. Where possible the results are generalised to non-Gaussian distributions. The theoretical results indicate that if the firm parameters are heterogeneous but come from a common distribution, for sufficiently large portfolios there is no scope for further risk reduction through active portfolio management. However, if the firm parameters come from different distributions, then further risk reduction is possible by changing the portfolio weights. In either case, neglecting parameter heterogeneity can lead to underestimation of expected losses. But, once expected losses are controlled for, neglecting parameter heterogeneity can lead to overestimation of risk, whether measured by unexpected loss or value-at-risk
Trombe walls with nanoporous aerogel insulation applied to UK housing refurbishments
There is an opportunity to improve the efficiency of passive Trombe walls and active solar air collectors by replacing their conventional glass covers with lightweight polycarbonate panels filled with nanoporous aerogel insulation. This study investigates the thermal performance, energy savings, and financial payback period of passive Aerogel Trombe walls applied to the existing UK housing stock. Using parametric modeling, a series of design guidance tables have been generated, providing estimates of the energy savings and overheating risk associated with applying areas of Trombe wall to four different house types across the UK built to six notional construction standards. Calculated energy savings range from 183 kWh/m2/year for an 8 m2 system retrofitted to a solid walled detached house to 62 kWh/m2/year for a 32 m2 system retrofitted to a super insulated flat. Predicted energy savings from Trombe walls up to 24 m2 are found to exceed the energy savings from external insulation across all house types and constructions. Small areas of Trombe wall can provide a useful energy contribution without creating a significant overheating risk. If larger areas are to be installed, then detailed calculations would be recommended to assess and mitigate potential overheating issues.The EPSRC, Brunel University, and Buro Happold Lt
Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models
We consider a class of generalized capital asset pricing models in continuous
time with a finite number of agents and tradable securities. The securities may
not be sufficient to span all sources of uncertainty. If the agents have
exponential utility functions and the individual endowments are spanned by the
securities, an equilibrium exists and the agents' optimal trading strategies
are constant. Affine processes, and the theory of information-based asset
pricing are used to model the endogenous asset price dynamics and the terminal
payoff. The derived semi-explicit pricing formulae are applied to numerically
analyze the impact of the agents' risk aversion on the implied volatility of
simultaneously-traded European-style options.Comment: 24 pages, 4 figure
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Optimal seismic upgrade timing in seaports with increasing throughput demand via real options
A real options (RO) formulation is proposed for decision-making on the timing to upgrade the seismic performance of existing seaports with increasing throughput demand in earthquake prone areas. The pay-off of the seismic upgrade investment option is estimated based on projected net earnings, repair cost, and downtime for a damaging reference seismic event having a pre-specified annual probability of occurrence. These projections inform a discrete-time RO binomial tree, following the American option valuation framework, which propagates the probability of the reference seismic event assuming Poisson temporal distribution of earthquake occurrence. The net present value of the expected annual payoff of the considered investment is used as an index supporting risk-informed decision-making discounted by the weighted average cost of capital (WACC). Numerical examples pertaining to decision makers with different capital cost, namely port authorities and terminal operators, operating in different economic environments typical of developed and developing countries are furnished to illustrate the applicability of the proposed RO formulation. It is found that high WACC and/or low throughput growth bring the optimal seismic upgrade timing forward, while earthquake consequences and upgrade cost have almost no influence on this timing
Derivatives and Credit Contagion in Interconnected Networks
The importance of adequately modeling credit risk has once again been
highlighted in the recent financial crisis. Defaults tend to cluster around
times of economic stress due to poor macro-economic conditions, {\em but also}
by directly triggering each other through contagion. Although credit default
swaps have radically altered the dynamics of contagion for more than a decade,
models quantifying their impact on systemic risk are still missing. Here, we
examine contagion through credit default swaps in a stylized economic network
of corporates and financial institutions. We analyse such a system using a
stochastic setting, which allows us to exploit limit theorems to exactly solve
the contagion dynamics for the entire system. Our analysis shows that, by
creating additional contagion channels, CDS can actually lead to greater
instability of the entire network in times of economic stress. This is
particularly pronounced when CDS are used by banks to expand their loan books
(arguing that CDS would offload the additional risks from their balance
sheets). Thus, even with complete hedging through CDS, a significant loan book
expansion can lead to considerably enhanced probabilities for the occurrence of
very large losses and very high default rates in the system. Our approach adds
a new dimension to research on credit contagion, and could feed into a rational
underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure
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