Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

Political Risk in Credit Evaluation: Empirical Studies and Survey Results

Financing trade between economic agents located in different countries is affected by many types of risks, resulting from incomplete information about the debtor, the problems of enforcing international contracts, or the prevalence of political and financial crises. Trade is important for economic development and the availability of trade finance is essential, especially for developing countries. Relatively few studies treat the topic of political risk, particularly in the context of international lending. This thesis explores new ground to identify links between political risk and international debt defaults. The core hypothesis of the study is that the default probability of debt increases with increasing political risk in the country of the borrower. The thesis consists of three essays that support the hypothesis from different angles of the credit evaluation process. The first essay takes the point of view of an international lender assessing the credit risk of a public borrower. The second investigates creditworthiness assessment of companies. The obtained results are substantiated in the third essay that deals with an extensive political risk survey among finance professionals in developing countries. The financial instruments of core interest are export credit guaranteed debt initiated between the Export Credit Agency of Finland and buyers in 145 countries between 1975 and 2006. Default events of the foreign credit counterparts are conditioned on country-specific macroeconomic variables, corporate-specific accounting information as well as political risk indicators from various international sources. Essay 1 examines debt issued to government controlled institutions and conditions public default events on traditional macroeconomic fundamentals, in addition to selected political and institutional risk factors. Confirming previous research, the study finds country indebtedness and the GDP growth rate to be significant indicators of public default. Further, it is shown that public defaults respond to various political risk factors. However, the impact of the risk varies between countries at different stages of economic development. Essay 2 proceeds by investigating political risk factors as conveivable drivers of corporate default and uses traditional accounting variables together with new political risk indicators in the credit evaluation of private debtors. The study finds links between corporate default and leverage, as well as between corporate default and the general investment climate and measeures of conflict in the debtor country. Essay 3 concludes the thesis by offering survey evidence on the impact of political risk on debt default, as perceived and experienced by 103 finance professionals in 38 developing countries. Taken together, the results of the thesis suggest that various forms of political risk are associated with international debt defaults and continue to pose great concerns for both international creditors and borrowers in developing countries. The study provides new insights on the importance of variable selection in country risk analysis, and shows how political risk is actually perceived and experienced in the riskier, often lower income countries of the global economy.

Analysis,Insights and Generalization of a Fast Decentralized Relay Selection Mechanism

Relay selection for cooperative communications has attracted considerable research interest recently. While several criteria have been proposed for selecting one or more relays and analyzed, mechanisms that perform the selection in a distributed manner have received relatively less attention. In this paper, we analyze a splitting algorithm for selecting the single best relay amongst a known number of active nodes in a cooperative network. We develop new and exact asymptotic analysis for computing the average number of slots required to resolve the best relay. We then propose and analyze a new algorithm that addresses the general problem of selecting the best Q >= 1 relays. Regardless of the number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. Our analysis also brings out an intimate relationship between multiple access selection and multiple access control algorithms.

Credit Default Swaps and Insurance: Against the Potts Opinion

Little attention has been given to the possibility that CDS transactions might be construed as insurance contracts in English law. This article challenges the widespread “Potts opinion”, which states that CDSs are not insurance, because they do not require the protection buyer to sustain a loss or to have an insurable interest in the subject matter. CDSs often do provide protection against loss that the buyer is exposed to; loss indemnity is not a necessary characterisation of an insurance contract; insurable interest does not form part of the definition of insurance, but is an additional requirement of valid insurance; and what matters is the substance not the form of the contract. The situation in the US and Australia is also briefly considered.

Application of nonlinear filtering to credit risk

Merton's model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihood estimation, but does pave the way for the `Expectation-Maximization' method for estimating parameters. (C) 2010 Elsevier B.V. All rights reserved.

Thermomechanical generalization of pin joints in finite plates

The understanding of thermoelastic behaviour of joints is significant in order to ensure the integrity of large and complex structures exposed to a thermal environment, particularly in fields such as aerospace and nuclear engineering. Thermomechanical generalization of partial contact behaviour of a pin joint under combined in-plane mechanical loading and on-axis unidirectional heat flow has already been established by the authors for the analytically simpler domains of large plates. This paper successfully extends the on-going investigation to a single pin in a finite rectangular isotropic plate as a two-dimensional abstraction from a practical situation of a multipin fastener joint. The finite element method is used to analyse the joint problem under on-axis thermomechanical loading and unified load-contact relationships are established for a class of loading conditions.

Generalization of Abrams' law

Considering cement based composites as chemically bonded ceramics (CBC) the consequent strength development with age is essentially a constant volume solidification process, such that the hydrated gel particles fill the space resulting in the compatible gel space ratios. Analysis has been done of the extensively used graphical method of mix design (British method of mix design) i.e., the relation between the compressive strength and the free water - cement ratio. By considering the strength (S) at w/c 0.5 (S-0.5) as the reference state to reflect the synergetic effects between constituents of concrete a generalized relationship obtained is of the form {S/S-0.5} = a + b {1/(w/c)}.

Thermomechanical generalization of partial contact in pin joints

Mechanical fasteners introduce structural weakness, still they are an essential constituent of most structures as they permit interchangeability of parts and flexible construction programs; Variable temperature operations of Aerospace and Nuclear structures make it imperative to investigate the thermoelastic behaviour of joints. This paper explores analytically similar mechanical and thermal parameters to generalise the thermomechanical behaviour of a pin joint in an isotropic Sheet for a class of configurations. This generalization enables virtually direct application of existing information regarding joints under pure mechanical loading to joints subjected to combined thermomechanical loading, thus reducing the efforts of both the analyst and the designer by an order of magnitude. Copyright (C) 1996 Published by Elsevier Science Ltd.

New Ventures’ influence on the Growth of SME Employment, Production and Exports in India: Does Institutional Credit matter?

New ventures are considered to be a major source of small firm growth. In Indian context the contribution of new ventures in terms of new employment, production and exports has largely remained unexplored. It is equally important and unexplored, the significance of the contribution of bank credit to the growth of new ventures in India. This paper is an attempt to throw light on these two aspects. The research is based on secondary data of the liberalized period provided by Ministry of Micro, Small and Medium Enterprises, Government of India and Reserve Bank of India. To analyze the influence of bank credit growth on new ventures and the influence of new ventures on growth of additional employment, additional production and additional exports, we used a Bi-Variate Vector Auto Regression. Based on the model generated, Granger causality tests are conducted to obtain the results. The study found that rate of growth of bank credit causes the number of new ventures, implying any increase in the rate of growth of bank credit will be beneficial to the growth of new ventures. The study also concluded that new ventures are not causing the growth of additional employment or additional production. However new ventures cause the growth of additional exports. This is reasonable as entrepreneurs start their new ventures with minimum possible employment and relatively low rate of capacity utilization and they come up to take advantage of the process of globalization by catering to the international market.

Generalization of the collision cone approach for motion safety in 3-D environments

Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.

Pricing credit derivatives

The financial crisis set off by the default of Lehman Brothers in 2008 leading to disastrous consequences for the global economy has focused attention on regulation and pricing issues related to credit derivatives. Credit risk refers to the potential losses that can arise due to the changes in the credit quality of financial instruments. These changes could be due to changes in the ratings, market price (spread) or default on contractual obligations. Credit derivatives are financial instruments designed to mitigate the adverse impact that may arise due to credit risks. However, they also allow the investors to take up purely speculative positions. In this article we provide a succinct introduction to the notions of credit risk, the credit derivatives market and describe some of the important credit derivative products. There are two approaches to pricing credit derivatives, namely the structural and the reduced form or intensity-based models. A crucial aspect of the modelling that we touch upon briefly in this article is the problem of calibration of these models. We hope to convey through this article the challenges that are inherent in credit risk modelling, the elegant mathematics and concepts that underlie some of the models and the importance of understanding the limitations of the models.