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This paper provides some theoretical foundations for using moving average (MA) rules in the stock market. In particular, the paper analyzes the conditional probability of price increments and examines how this probability varies over time. We prove under certain assumptions that the probability of being in an uptrend is greater than the probability of being in a downtrend. This demonstration partially justifies the common use of MA rules in the stock market. Finally, we propose an ex-post empirical analysis to evaluate and compare the performance of some MA rules and other portfolio strategies in the US stock market. In this context, we also suggest a methodology that incorporates these trading rules as alarm rules to predict potential market failures. Our ex-post results confirm the advantages of using these trading rules to predict market trends and crises.

Statistical models of football (soccer) match outcomes have potential applications to areas such as the development of team rankings and football betting markets. Much of the published work in this context has typically focused on the use of generalized linear models, which are non-dynamic in the sense that the parameters in the model, which often represent the underlying abilities of each team, are assumed to remain constant over time. Dynamic generalized linear models (DGLMs) on the otherhand allow the abilities of each team to vary over time. This paper illustrates the application of a DGLM in the context of football match outcome prediction and describes improvements on similar work previously presented by the author, in relation to the estimation of a parameter in the model, referred to as the evolution variance, which is crucial in terms of optimizing the predictive performance of these types of models. Match results data from the Scottish Premier League from 2003/2004 to 2005/2006 are used to show that the DGLM approach provides improved predictive probabilities of future match outcomes compared to the non-dynamic form of the model. DGLMs are also Bayesian in terms of their structure and so a Bayesian approach to parameterestimation is required. This paper therefore illustrates a practical implementation of the DGLM model that can easily be deployed using the freely available software WinBUGS.

This paper provides the first optimal portfolio analysis for a constant relative risk-averse and ambiguity-averse investor under the state-of-the-art 4/2 stochastic volatility model in a complete market setting. We determine the robust optimal strategy and the worst case measure by allowing separate levels of uncertainty for variance and stock drivers. Technical conditions for well-defined solutions are detailed together with a verification result. The robust optimal investment exposure displays a dependence on current volatility levels similar to the non-robust case further impacted by the ambiguity-aversion level. Using real-world parameters, the numerical analysis finds that wealth-equivalent losses (WELs) from ignoring uncertainty or market completeness are moderate. On the other hand, WELs for investors who follow simpler but popular strategies, such as Heston (1/2 model) and Merton (geometric Brownian motion [GBM] model), could be quite substantial, of up to 24 and 51%, respectively. This latest analysis comes from new non-affine representations for the suboptimal value function of the 1/2 and GBM strategies.

In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.

In this paper, the pricing of foreign exchange options is considered under a modified Heston–Cox–Ingersoll–Ross hybrid model. This modified model reserves all the characteristics of the Heston–Cox–Ingersoll–Ross model and also additionally assumes regime switching in the key parameters of the volatility as well as the domestic and foreign interest rates. Even though complicated, we have derived a closed-form pricing formula for foreign exchange options after the affinity of this new model is verified. Various properties of the newly derived formula are also shown through numerical experiments. To show the performance of this newly proposed model, an empirical study is also conducted, the result of which suggests that our model is a good alternative to the Heston–Cox–Ingersoll–Ross model for practical purpose.

This paper contributes to the research on multi-pillar pension systems with main focus on private pension funds (PFs). In this context, the specific objective of this study is to determine which second-pillar private fund is the best for participants in such systems on the basis of their risk profile. Based on the assumptions on utility functions of the participants in a pension scheme, four types of stochastic dominance (SD) relations are considered, specifically first order, second order, third order and SD generated by utility functions with decreasing absolute risk aversion. We conduct an analysis under two distributional assumptions: empirical and stable distribution of returns. Moreover, the investors for which non-dominated funds are the optimal choices are identified. Allowing for diversification, the efficiency of the PFs with respect to several types of SD is tested. Then, the observed behaviour of participants in the last quarter/year is compared to the results of SD analysis. Finally, the identified SD relations are stress-tested using data originating from a period of turmoil. Despite the focus on Lithuanian PFs, the methodology developed in this work can be employed by participants or PF managers in similar markets of other countries.

The interest rate and the market price of risk may be stochastic in a real-world financial market. In this paper, the interest rate is assumed to be driven by a stochastic affine interest rate model and the market price of risk from the stock market is a mean-reverting process. In addition, the dynamics of the stock are simultaneously driven by random sources of interest rate and the stock market itself. In pension fund management, different fund managers may have different risk preferences. We suppose risk preference is described by the hyperbolic absolute risk aversion utility, which is a general utility function describing different risk preferences. Legendre transform-dual theory is presented to successfully obtain explicit expressions for optimal strategies. A numerical example illustrates the sensitivity of optimal strategies to market parameters. Theoretical results imply that the risks from stochastic interest rate and stochastic return may be completely hedged by adopting specific portfolios.

Mathematical models are often used to describe the sales and adoption patterns of products in the years following their launch and one of the most popular of these models is the Bass model. However, using this model to forecast sales time series for new products is problematical because there is no historic time series data with which to estimate the model’s parameters. One possible solution is to fit the model to the sales time series of analogous products that have been launched in an earlier time period and to assume that the parameter values identified for the analogy are applicable to the new product. In this paper, we investigate the effectiveness of this approach by applying four forecasting methods based on analogies (and variants of these methods) to the sales of consumer electronics products marketed in the USA. We found that all the methods tended to lead to forecasts with high absolute percentage errors, which is consistent with other studies of new product sales forecasting. The use of the means of published parameter values for analogies led to higher errors than the parameters we estimated from our own data. When using our own data, averaging the parameter values of multiple analogies rather than relying on a single most-similar, product led to improved accuracy. However, there was little to be gained by using more than five or six analogies.

In inventory management, hierarchical forecasting (HF) is a hot issue: families of items are formed for which total demand is forecasted; total forecast then is broken up to produce forecasts for the individual items. Since HF is a complicated procedure, analytical results are hard to obtain; consequently, most literature is based on simulations and case studies. This paper succeeds in following a more theoretical approach by simplifying the problem: we consider estimation instead of forecasting. So, from a random sample we estimate both the total demand and the fraction of this total that individual items take; multiplying these two quantities gives a new estimate of the individual demand. Then, our research question is: Can aggregation of items, followed by fractioning, lead to more accurate estimates of individual demand? We consider two simple situations that can be analysed fully theoretically. Thirdly, a more practical situation is investigated by means of simulation.

In this paper we propose using computational tests for appraising the inaccuracies of index numbers (for example, price and wage indices). This is done by programming a hypothetical situation where the true average index value is known and the variation of prices and quantities and the relation between them can be chosen. The indices are then calculated using the formulae of Laspeyres, Paasche, Fisher, the Unit index and Normalized Unit index formulae. By comparing the average values of the above formulae with the true average index value, we are able to obtain a quantitative indication of the errors in these formulae under various situations. The Normalized Unit and Fisher index formulae were found to be consistently accurate for all our tests whereas the formulae of Laspeyres and Paasche were found to have very poor accuracy in the majority of our tests. The Unit index was also consistently accurate in all our tests but its use is appropriate in the single item case thus making this formula suitable for measuring wages. In our informal discussion of stability we indicated that the Normalized unit index and the Unit index have good stability characteristics whereas the indices Laspeyres, Paasche and Fisher have poor stability characteristics. In view of the above the Normalized Unit index is the best of the formulae we have discussed for measuring prices (many item case), and the Unit index is the best of the formulae we have discussed for measuring wages (single item case).