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We determine the functional forms of a class of multiattribute utility functions that lead to zero-switch change in preferences between multi-period cash flows when a decision maker's initial wealth increases through an annuity that pays a constant amount every time period.
We consider a class of multiattribute utility functions which are invariant with respect to the shifts having identical parameters for each attribute.
The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for the detailed study of the tail behaviour of the multivariate copulas. In this paper we investigate the class of copulas being the weighted means of copulas having homogeneous lower tails. We show that having only such information on the structure of dependence of returns from assets is enough to get estimates on value at risk of the multiasset portfolio in terms of value at risk of one-asset portfolios.
We proposed a model of interacting market agents based on the generalized Ising spin model. The agents can take three actions: "buy", "sell", or "stay inactive". We defined a price evolution in terms of the system magnetization. The model reproduces main stylized facts of real markets such as: fat-tailed distribution of returns and volatility clustering.
In this paper, we try to model the dynamics of short term interest rate using the fractional nonhomogeneous differential equation with stochastic free term. This type of equation is similar to one which represents the viscoelastic behavior of certain materials from rheologic point of view. As a final result we obtain the closed formula for prices of zero-coupon bonds. They are analogous to those in Vasiček model, where instead of the exponential functions we have the Mittag-Leffler ones.
A utility function U is said to be invariant with respect to a family of transformations Γp provided, for every member γ of Γp, U and Uırc γ represent the same preference relation over lotteries. An invariance with respect to a wide class of transformations can be reduced to an invariance with respect to the shift transformations. We give a complete answer to the following question: given a nonempty set T of shifts determine all utility functions invariant with respect to the shift transformations by every element of T. As a consequence of our results we obtain the forms of utility functions invariant with respect to the families of commuting transformations.
In this study, we consider a minimum-variance hedging problem in an incomplete market, in which the risky asset is driven by the process based on non-extensive statistical mechanics and Poisson jumps. Using the stochastic control theory and backward stochastic differential equation method, we obtain a closed-form solution for the minimum-variance hedging policy.
We prove the existence of the Foster-Hart measure of riskiness under the cumulative prospect theory and we study some of its basic properties.
We prove that if the principle of equivalent utility under the cumulative prospect theory is positively homogeneous on a relatively small family of risks for every non-negative initial wealth level, then a value function is linear for gains and losses, but, in general, it needs not be linear.
Long memory has always played a central role in physics since it was first discovered by Hurst while studying the flow of the River Nile. Interestingly, after his seminal work, many other researchers found the same pattern in other domains of science, such as biology, economics and finance. These studies have mainly relied on the use of the Hurst exponents as a measure of the degree of memory in a process. In this paper we use a different approach based on the FIGARCH (fractional integrated generalized autoregressive conditionally heteroskedasticity) model proposed by Baillie et al. in order to analyze the long memory behavior of stock market volatility. More specifically, we compare how the long memory parameter evolves before and after the 2008 and 2012 crises in both developed and emerging markets. Specifically, we consider the daily returns of the S&P 500, STOXX 50, FTSE 100, NIKKEI 225, HSI, BUX, WIG, SSE, IDX and KLCI indices for the period from October 1, 2003 to October 2, 2015 and then split the whole sample into four sub-samples of roughly three years each. Results show different patterns for the pre and post crisis periods revealing that the degree of memory differs in accordance with the country's development and the level of market turbulence. In particular, we found that major mature economies present higher levels of long memory than emerging countries and were more affected by the 2008 and 2012 crises.
In credit risk scoring models are used as a tool to evaluate the level of risk associated with applicants or customers. The aim of these models is not only to estimate the probability that the client will not be able to fulfill his financial commitments but also to identify and estimate the risk drivers i.e., client attributes that are responsible for risk occurrence. Unfortunately, scoring models are built based on historic data stored by bank over the clients. Selection of clients is not random. This leads to systematic errors. Therefore one seeks methods that allow for a model correction that enables application of statistical inference. Quasi-experimental designs are practical solutions to this dilemma. One of such methods is propensity score matching. Propensity score matching allows also for detecting risk drivers that are independent of borrowers attributes, e.g., triggered by various bank strategies. The aim of our research is to apply propensity score matching methodology to identify these risk drivers in credit risk that could not be detected e.g., by regression models.
The traditional method of analysing a time series of stocks and funds is to use simple Pearson correlations. However, experience shows that cross-correlations are not an accurate indicator of the mutual ownership relations. We show that the minimum spanning tree methodology, previously used to perform more comprehensive studies of asset returns correlations, can be used to deduce the underlying ownership structure with reasonable accuracy. We also show that adjusting the time series for a common trend of stocks and subsequent filtering of the short term variations of returns using the ARIMA model is a prerequisite for this application of the minimum spanning tree.
In 1984 A. Reich proved that under Expected Utility Theory, a scale invariance of the Principle of Equivalent Utility just for two particular values of parameters implies its scale invariance. In this paper, we extend this result onto the Principle of Equivalent Utility under Cumulative Prospect Theory.
We investigate the dynamics of inter-order durations, i.e. times elapsing between consecutive orders submitted to the Reuters Dealing 3000 Spot Matching System, an automated brokerage platform for interbank EUR/PLN spot trading. Strong autocorrelation of the inter-order waiting times combined with the significant cross-correlations among individual order types (i.e. market buy, market sell, limit buy, limit sell) has been captured with the Mulistate Asymmetric Box-Cox Autoregressive Conditional Duration (MABCACD) model. Our empirical study provides new insights about the microstructure of the interbank FX spot markets.
The objective of this study is to verify the existence of the spillover effects within the complex system of internationally co-integrated real estate and financial markets in the case of the growth rates of the price indices of the direct real estate and indirect real estate investment markets within the selected national economies in the CEE region and to discuss the time stability of their directions, using research methods with physics and econometrics origins. The article considers the case of potential spillover effects between the Polish and Austrian national economies. Presented results have been obtained using wavelet analysis methods, such as wavelet coherency, wavelet phase difference, and wavelet partial phase difference analyses, enabling to check the indicated stability both in the time and frequency domains and to detect any potential structural changes dates. The results have not confirmed the hypotheses that the directions of the mentioned spillover effects displayed time stability in the examined period (Q4 2004-Q4 2014), which disproves the usefulness of the knowledge of the current directions of the indicated effects in the scope of performing long term investment policy, as well as in the scope of projecting the long term internal housing policies and long term internal macroprudential policies within the complex system.
The model discussed in this paper is a modification of the model of macroeconomic evolution in stable regionally dependent fields, developed by Ausloos, Clippe and Pekalski in 2004. Like in the original model, firms exist on a square lattice and can move, merge, adapt and create spin-offs. However, in the new model the firms are described by a scalar parameter identified with their level of technology and by their market share. The probability of survival of a firm depends on the relation between the firm's technology level and the level of the technological frontier. The model incorporates two mechanisms of technology diffusion - inner (resulting from the cooperation between firms and the creation of spin-offs) and outer (interaction with the technological frontier). In this way, we obtain a model of technological progress with technology diffusion. We investigate the properties of this model and perform empirical analysis for a group of OECD countries.
In this work we compared the empirical data of annual income of Polish and European households as well as annual income of individuals in United States (e.g. for years 2006 and 2008) with predictions of the most popular theoretical models. Particularly good agreements with Pareto distribution and prediction of the Yakovenko model were obtained. For the low society class well agreement with prediction of the cumulative exponential distribution was gained. However, it turned out that the cumulative distribution of annual income of Polish households can be described quite well by the Generalised Lotka-Volterra model.
The non-extensive entropy (NEE) principle has been successfully applied in the case of high frequency financial market analysis. I try to extend the approach to empirical social sciences and propose a competitive estimation approach with respect to classical econometrical methods. This article constitutes a limited extension of Jaynes-Shannon-Gibbs' (JSG) ergodic system formalism already applied to classical econometrics. The Podkarpackie private labour demand model is then developed and its outputs presented. A constrained weighted dual criterion function maximising entropy probabilities for parameter and disturbance components is derived and its inferential information indexes are proposed and computed. We note that the increase of relative weights on disturbance component leads to higher values of q, the entropic index of generalized Tsallis entropy. Smaller disturbance weights produce q values closer to unity. Outputs then converge to those displayed by the competitive JSG and least squares (LS) approaches. However, finding out an inferential rule delimiting the critical q values for Gaussian distribution interval remains of high interest. In terms of economics, the results of the proposed model show a realistic adjusting speed mechanism of actual lever of employment to its long run targeted equilibrium level owing to expected market profits.
At the end of 19th century Vilfredo Pareto, as the first tried by using power-laws to describe wealth and income distributions in society. We applied early works of Pareto as well as Gibrat (i.e. laws of Pareto and rules of proportionate growth, respectively). Furthermore, we used recent and advanced models: the Generalised Lotka-Volterra model and collision models. By using empirical data for annual income of Polish households, e.g. for years 2003 and 2006, the comparison with these theoretical models was successfully made. The surprisingly good agreements with Pareto distribution were obtained, where Pareto exponents near the cubic law were found for middle class. For the low class very good agreement with prediction of the cumulative log-normal distribution was gained. Hence, it was possible to establish the border between low and middle society levels. The same was possible for the border between high and middle classes as the ranking for the former follows (to some extent) the Zipf law.
Indices of selected financial markets from various parts of world, different sizes and levels of development are investigated. The local Hurst exponent is globally compared to log-prices. Periodic changes in correlation coefficient are quantified via discrete Fourier transform. Local Hurst exponents spectra are discussed for investigated markets.
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