Browsing by Author "Guerra, Manuel"
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- An horizontal innovation growth model with endogenous time allocation and non-stable demographyPublication . Guerra, Manuel; Pereira, João; St. Aubyn, MiguelWe propose a decentralized endogenous growth model in order to study the transitional dynamics associated with the process of population aging in a small open economy. The model features endogenous time allocation and two growth engines: R&D and human capital accumulation. Per capita output growth is affected negatively by the difference in the rates of growth of labor force and of the total population in the period where the weight of the labor force decreases to a new and lower level. The biggest impact of aging on per capita output growth is during the period where labor force grows at a lower rate than the population unless it is compensated by some other effect. Under some assumptions, a decrease in the corporate tax improves growth.
- Are quantile risk measures suitable for risk-transfer decisions?Publication . Guerra, Manuel; Centeno, M. de LourdesAlthough controversial from the theoretical point of view, quantile risk measures are widely used by institutions and regulators. In this paper, we use a unified approach to find the optimal treaties for an agent who seeks to minimize one of these measures, assuming premium calculation principles of various types. We show that the use of measures like Value at Risk or Conditional Tail Expectation as optimization criteria for insurance or reinsurance leads to treaties that are not enforceable and/or are clearly bad for the cedent. We argue that this is one further argument against the use of quantile risk measures, at least for the purpose of risk-transfer decisions.
- Life cycles with endogenous time allocation and age-dependent mortalityPublication . Guerra, Manuel; Pereira, João; St. Aubyn, MiguelThe negative effect of population aging on the economy can be mitigated by a behavioral effect of people as a reaction to a higher life expectancy. We analyze the optimal life-cycle of individuals that allocate time at the intensive margin between leisure, human capital accumulation, and labor supply while facing an age-dependent mortality. This allows to enhance effects of changes in life expectancy on labor supply and human capital accumulation and to uncover trade-offs between time allocations at different stages of the life-cycle. Our life-cycles are characterized by on the job training throughout all the working life with a possibility of a temporary exit from the labor market. We simulate the model numerically and find that with a higher life expectancy, labor supply increases at the intensive margin and the individual invests more in human capital. We also find a willingness to increase labor supply at the extensive margin.
- Market timing with option-implied distributions in an exponentially tempered stable Lévy marketPublication . Guerra, João; Guerra, Manuel; Polaski, ZacharyThis paper explores the empirical implementation of a dynamic asset allocation strategy using option-implied distributions when the underlying risky asset price is modeled by an exponential Lévy process. One month risk-neutral densities are extracted from option prices and are subsequently transformed to the risk-adjusted, or real-world densities. Optimal portfolios consisting of a risky and risk-free asset rebalanced on a monthly basis are then constructed and their performance analyzed. It is found that the portfolios formed using option-implied expectations under the Lévy market assumption, which are flexible enough to capture the higher moments of the implied distribution, are far more robust to left-tail market risks and offer statistically significant improvements to risk-adjusted performance when investor risk aversion is low, however this diminishes as risk aversion increases.
- Mathematical control theory and FinancePublication . Sarychev, Andrey; Shiryaev, Albert; Guerra, Manuel; Grossinho, Maria do RosárioControl theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.
- Optimal per claim reinsurance for dependent risksPublication . Guerra, Manuel; Centeno, M. de LourdesThis paper generalizes the results on optimal reinsurance pre sented in Centeno and Guerra (2008) to the case of an insurer holding a portfolio of k dependent risks. It is assumed that the number of claims of a risk may depend on the number of claims of the other risks of the portfolio. Our aim is to determine the optimal form of reinsurance for each risk when the cedent seeks to maximize the adjustment coefficient of the retained portfolio - which is equivalent to maximizing the expected utility of wealth, with respect to an exponential utility with a certain coefficient of risk aversion - and restricts the reinsurance strategies to functions of the individual claims. Assuming that the premium calculation principle is a convex functional we prove existence and uniqueness of solutions and provide a necessary optimality condition. These results are used to find the optimal reinsurance policy for a given risk when the reinsurance loading is either proportional to the expected value or increasing with the variance of the ceded claims. The type of the optimal arrangement for a given risk only depends on the premium of that particular risk.
- Optimal reinsurance policy : The adjustment coefficient and the expected utility criteriaPublication . Guerra, Manuel; Centeno, M. de LourdesThis paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer. Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.
- Optimal trading under coherent comonotonic risk measuresPublication . Guerra, Manuel; Centeno, M. de LourdesThis paper deals with the optimal risk trading from the point of view of an individual who rates his position using a coherent comonotonic risk measure, assuming that the market price is also coherent and comonotonic. We obtain a simple and intuitive explicit solution in terms of Kusuoka representation
- The optimal reinsurance strategy : the individual claim casePublication . Centeno, M, de Lourdes; Guerra, ManuelThis paper is concerned with the optimal form of reinsurance when the cedent seeks to maximize the adjustment coefficient of the retained risk (related to the probability of ultimate ruin) – which we prove to be equivalent to maximizing the expected utility of wealth, with respect to an exponential utility with a certain coefficient of risk aversion – and restricts the reinsurance strategies to functions of the individual claims, which is the case for most nonproportional treaties placed in the market. Assuming that the premium calculation principle is a convex functional we prove the existence and uniqueness of solutions and provide a necessary optimality condition (via needle-like perturbations, widely known in optimal control). These results are used to find the optimal reinsurance policy when the reinsurance loading is increasing with the variance. The optimal contract is described by a nonlinear function, of a similar form than in the aggregate case.