This paper considers a continuous-time economic equilibrium model for deriving the economic premium principle of Buhlmann and Iwaki, Kijima and Morimoto. In order to do this, we construct a continuous-time consumption/portfolio model, and consider an equilibrium in a pure-exchange economy. The state price density in equilibrium is obtained in terms of the Arrow-Pratt index of absolute risk aversion for a representative agent. As special cases, power and exponential utility functions are examined, and we derive an endogenously decided equilibrium insurance premium in explicit form.

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Under the continuous-time framework with incomplete information on asset price processes, we show that the universal portfolio coincides with the optimal Bayes portfolio, which have been studied intensively in the financial economics literature. That is, we can interpret the universal portfolio as simultaneously estimating the drift and controlling the portfolio. This result holds in the finite terminal-time setting of the investment horizon. Moreover, we investigate the asymptotic behavior of the universal portfolio along its original definition and obtain a result that in the long run, the universal portfolio with incomplete information converges to the optimal portfolio with complete information.

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Conventionally, linear and univariate time series models are broadly used in earning forecast. However, their forecasting accuracies are seriously limited without considering sufficient important factors. On the other hand, using more variables does not guarantee to obtain better forecasting accuracy and may cause inefficiency. The Multi-Objective Genetic Algorithms (MOGA) have been shown to be able to select the variable set with population diversity and to perform efficient search in large space. In addition, the multiple regression model can efficiently evaluate the predicting accuracy by using the least sum of squared errors (SSE). We therefore combine the advantages of both multiple regression and MOGA to form a new efficient forecasting mechanism which maximizes the forecasting accuracy with minimal number of financial ratios. Furthermore, this mechanism includes the SWMR (Sliding Window Multiple Regression) mechanism which retrains our predictor periodically in order to get more accurate earning forecast.

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Research and development projects in the pharmaceutical industry normally last for a decade, require a large amount of investment and are highly risky. During the early stages of development, a company can seldom tell which chemical compound will successfully pass all subsequent stages and eventually become a marketable drug. Moreover, the long development process makes it difficult to predict the value of the marketable drug. The Net Present Value (NPV) method, used in most pharmaceutical companies to value their research and development projects, does not take into account the value of managerial flexibility. Examples of managerial flexibility include the right to stop or to make changes during the life of a project. Real-option evaluation expands the NPV method to embody the notion of managerial flexibility. For long-term projects, managers act upon new information revealed in the future and thus the real options approach better suits the decision making process in R &D management. In this article, we compute the value of an ongoing R&D project at Nihon Schering Kabushiki Kaisha (Nihon Schering). We show that, at the pre-clinical stage, the project had a negative value when evaluated under the traditional NPV method but a slightly positive value under the real-option approach. The difference comes from the recognition of "real options" embedded in the project. We conclude that real-option evaluation provides for a relevant and reliable method for reviewing a company's internal projects.

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This article examines the valuation problem for the European option under a general stochastic volatility in a certain approximate sense by adopting the small disturbance asymptotic theory developed by Kunitomo and Takahashi. The option value can be decomposed into the Black and Scholes value under deterministic volatility and adjustment terms driven by the randomness of the volatility, which also extends some portions of Kunitomo and Kim.

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Pricing American options is a difficult task due to the early exercise opportunities, and the higher the dimension. i.e. the number of underlying assets, is, the more complicated the problem is. Broadie and Glasserman proposed a Monte Carlo method for pricing American style options by using random trees. Their method has a merit that its computational complexity is linear in the dimension of the problem, but it often shows a slow convergence. In this paper, we propose a method making use of low-discrepancy sequences instead of random numbers to construct trees, based on which we obtain the estimate of the option price. We will present the detail of our "quasirandom tree method," and compare the random tree method with our method in pricing some American style options of high dimensionality. Our numerical experiments show a rapid convergence of our quasirandom tree method.

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New derivative products usually have complex payoff structures depending on multiple risk factors. In such situation numerical computation methods, such as Monte Carlo and quasi-Monte Carlo methods, become very powerful tools because of difficulty in evaluating their pricing model analytically. Low discrepancy sequences installed in quasi-Monte Carlo methods make it possible to produce the uniformity of distribution over the domain of integration, i.e. one or more dimensional unit cube, even for a small number of sample points, which makes numerical integrations to be efficient. Classical low discrepancy sequences, e.g. Faure sequences, are not always satisfactory for multi-dimensional integrations. However, some of generalized Faure sequences can attain quite high performance to compute high-dimensional integrations practically required in financial derivatives pricing, which have been reported in some papers. Unfortunately, none of detailed techniques for the practical construction of such high performanec generalized Faure sequences is shown in them. Incidentally, we can confirm that applying a kind of randomization to the classical sequences leads to realize better convergence performance than the original sequence, as we have reported. And recently, some error estimation methods for quasi-Monte Carlo simulation were proposed and experiments taking up such error estimations in numerical evaluations were reported. These methods require certain probabilistic structures of their internal sequences and the most generalized class of them demands huge computational quantity, which is a major problem to be solved in analyzing the quasi-Monte Carlo errors. In this paper, we try to modify low discrepancy sequences with randomized structures originally based on generalized Niederreiter sequences, to keep their performance of convergence and apply the quasi-Monte Carlo error estimation method to it. The structure of this sequence is simple, which can reduce computational complexity. These simplified sequences are applied to the numerical evaluation of path-dependent options in order to compare other low discrepancy and pseudo-random number sequences. We demonstrate that the sequences we proposed attain comparable performance of convergence, error estimation and evaluation time to sequences with more generalized and complicated probabilistic structures.

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In this study, we measure the fractal dimension of dollar/yen exchange rates for each week. The tick-by-tick data set of the bid/ask prices submitted by the brokers is used. For analyzing the data, we use two time scales: the physical time and the number of the submitted prices. The data are resampled to one-minute interval when the physical time is used. Using the number of the submitted prices, we can analyze all the data in the order of the records. We calculate the fractal dimensions on this two time scales by Higuchi's method. The main results are as follows. The weekly fractal dimensions vary with time. The fluctuations of the prices tend to have rather strong self-similarity when the market is volatile. The self-similarity is stronger on the physical time than on the number of prices. By using either time scale, the measured fractal dimensions exceed 1.5, which suggest anti-persistence. For any week, this anti-persistence is stronger on the number of the prices than on the physical time. However, the differences between these two dimensions of the same week little vary with time, since the variations of the two synchronize.

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I consider a participating policy as a contingent claim whose payoff is similar to a call option. The underlying asset of the claim is an asset portfolio continuously controlled by an insurance company. I derive an efficient frontier of the equity return of the company, as well as the trading strategy to realize efficient portfolios, by utilizing the martingale method for optimal portfolio selection problems. Some numerical examples indicate that the higher expected rate of return of the company is required, the more investment in risky assets is needed, and that probability of bonus payment is positive.

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This paper summarizes the authors' papers on the comparative analyses of expected shortfall and value-at-risk. It discusses the properties of risk measures in terms of (1) elimination of tail risk; (2) consistency with expected utility maximization; (3) subadditivity (convexity); and (4) stability on estimation. It examines whether expected shortfall and value-at-risk satisfy these properties, and shows that expected shortfall is superior to value-at-risk in terms of (1), (2), and (3), but inferior to value-at-risk in terms of (4).

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To decide the investment policy of a pension fund, a plan sponsor first conducts an asset allocation study and then he/she hires active managers to add active return to the portfolio. In order to seek active return, a plan sponsor must necessarily accept risk. But how much risk does the plan sponsor have to take, and how many managers does he/she have to hire? This problem that a plan sponsor often faced with is a manager selection problem. A lot of methods to decide the manager structure have been proposed, however, in the most cases the returns of the active funds are assumed to be normally distributed. In this study I empirically show that the returns of actively managed funds are not normally distributed and a plan sponsor is impossible to optimize the, manager structure by using the standard mean variance model. To accurately capture the risk of the funds, I use the target semi-deviation as a measure of risk. In my framework, shortfall below the return of policy asset mix is recognized as risk, and manager's active alpha is adjusted by the target semi-deviation. I also propose a method to decompose a portfolio's target semi-deviation for converting the optimal manager structure into the optimal risk allocation.

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Simulated path model was proposed by Hibiki(2001) in order to solve a multi-period optimization problem. We can use sample paths associated with asset returns using Monte Carlo simulation, and get a better accuracy of uncertainties. To meet non-anticipativity conditions, we cannot make conditional decision as in the scenario tree model, and therefore we must decide an optimal portfolio with a fixed-unit strategy. The original formulation of simulated path model does not use the decision rule with the fixed-unit strategy effectively. Though decision variables of risky asset depend on only the number of periods, respectively, the number of the decision variables of cash must depend on the set of paths and periods, and then leads to large-scale problems. In this paper, we propose a more compact formulation than the previous formulation by eliminating the decision variables of cash. This does not mean that cash is excluded from the asset allocation decision. We expect that computation time decreases by reducing the problem size. We call this formulation compact representation, and show two kinds of formulations. We examine several numerical examples in order to compare computation time of the compact form with that of original form.

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