This paper solves a long-standing open problem in mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is indeed possible if the dual problem and its domain are carefully defined. More precisely, we show that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form of the regular part of an element of(L∞)* (the dual space of L∞). (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

We show that, for a utility function U: R to R having reasonable asymptotic elasticity, the optimal investment process H. S is a super-martingale under each equivalent martingale measure Q, such that E[V(dQ/dP)] < "unendlich", where V is conjugate to U. Similar results for the special case of the exponential utility were recently obtained by Delbaen, Grandits, Rheinländer, Samperi, Schweizer, Stricker as well as Kabanov, Stricker. This result gives rise to a rather delicate analysis of the "good definition" of "allowed" trading strategies H for the financial market S. One offspring of these considerations leads to the subsequent - at first glance paradoxical - example. There is a financial market consisting of a deterministic bond and two risky financial assets (S_t^1, S_t^2)_0<=t<=T such that, for an agent whose preferences are modeled by expected exponential utility at time T, it is optimal to constantly hold one unit of asset S^1. However, if we pass to the market consisting only of the bond and the first risky asset S^1, and leaving the information structure unchanged, this trading strategy is not optimal any more: in this smaller market it is optimal to invest the initial endowment into the bond. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Bitcoin is an unregulated digital currency originally introduced in 2008 without legal tender status. Based on a decentralized peer-to-peer network to confirm transactions and generate a limited amount of new bitcoins, it functions without the backing of a central bank or any other monitoring authority. In recent years, Bitcoin has seen increasing media coverage and trading volume, as well as major capital gains and losses in a high volatility environment. Interestingly, an analysis of Bitcoin returns shows remarkably low correlations with traditional investment assets such as other currencies, stocks, bonds or commodities such as gold or oil. In this paper, we shed light on the impact an investment in Bitcoin can have on an already well-diversified investment portfolio. Due to the non-normal nature of Bitcoin returns, we do not propose the classic mean-variance approach, but adopt a Conditional Value-at-Risk framework that does not require asset returns to be normally distributed. Our results indicate that Bitcoin should be included in optimal portfolios. Even though an investment in Bitcoin increases the CVaR of a portfolio, this additional risk is overcompensated by high returns leading to better return-risk ratios.

In recent years socially responsible investing has become an increasingly more popular subject with both private and institutional investors. At the same time, a number of scientific papers have been published on socially responsible investments (SRIs), covering a broad range of topics, from what actually defines SRIs to the financial performance of SRI funds in contrast to non-SRI funds. In this paper, we revisit Markowitz' Portfolio Selection Theory and propose a modification allowing to incorporate not only asset-specific return and risk but also a social responsibility measure into the investment decision making process. Together with a risk-free asset, this results in a three-dimensional capital allocation plane that allows investors to custom-tailor their asset allocations and incorporate all personal preferences regarding return, risk and social responsibility. We apply the model to a set of over 6,231 international stocks and find that investors opting to maximize the social impact of their investments do indeed face a statistically significant decrease in expected returns. However, the social responsibility/risk-optimal portfolio yields a statistically significant higher social responsibility rating than the return/risk-optimal portfolio.

Following [10] we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In [10] we proved that a minimal condition on the utility function alone, i.e. a minimal market independent condition, is that the asymptotic elasticity of the utility function is strictly less than 1. In this paper we show that a necessary and sufficient condition on both, the utility function and the model, is that the value function of the dual problem is finite. (authors' abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Si bien el CAPM no requiere que beta sea estable en el tiempo, al trabajar con series de datos y estimar su valor en el contexto del Modelo de Índice Simple, la estabilidad del coeficiente se torna en una condición crucial para su adecuada utilización. Una práctica ampliamente difundida consiste en obtener los valores a través de MCO, asumiendo la estabilidad de dicho coeficiente. El presente trabajo estima los coeficientes beta de portafolios de sectores económicos con oferta pública de acciones en la Bolsa de Comercio de Buenos Aires en el período 1994-2007, introduciendo una metodología de estimación no paramétrica denominada <i>Varying Coefficient Model</i>. El ejercicio muestra la importante volatilidad de los betas, siendo que es por ello altamente recomendable tomar con especial cuidado las estimaciones de betas basadas en datos históricos al querer extrapolarlas en el tiempo. La utilización en esta dirección, puede modificar drásticamente las conclusiones en la práctica de la administración de portafolios de inversión y en la valuación de empresas. Dos ejemplos de estas aplicaciones son mostradas en el anexo.

We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heuristic global optimization techniques. We benchmark the model against a GLMM model in the context of bond portfolio risk management. The proposed model yields stronger dependencies and higher risks than the GLMM model. As a result, the risk optimal portfolios are more conservative than the decisions resulting from the benchmark model.