Multi-asset investment-consumption model with transaction costs

In this paper, we consider the multi-asset optimal investment-consumption model: a riskless asset and d risky assets. when the initial time is t?0, for a proportional transaction costs and discount factors, we proof that the value function of the model is a unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equations.     

Geometry of financial markets—Towards information theory model of markets

Most parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems to be the correct language to describe the theater of financial activities. We suppose that the objects of interest of agents, called here baskets, form a vector space over the reals. A portfolio is defined as an equivalence class of baskets containing assets in the same proportions. Therefore portfolios form a projective space. Cross ratios, being invariants of projective maps, form key structures in the proposed model. Quotation with respect to an asset Ξ (i.e. in units of Ξ) is given by linear maps. Among various types of metrics that have financial interpretation, the min-max metric on the space of quotations can be introduced. This metric has an interesting interpretation in terms of rates of return. It can be generalized so that to incorporate a new numerical parameter (called temperature) that describes agent's lack of knowledge about the state of the market. In a dual way, a metric on the space of market quotation is defined. In addition, one can define an interesting metric structure on the space of portfolios/quotation that is invariant with respect to hyperbolic (Lorentz) symmetries of the space of portfolios. The introduced formalism opens new interesting and possibly fruitful fields of research.     

Mathematical analysis of the Miller-Modigliani theory

This paper provides a rigorous mathematical treatment of the problem of valuation of a firm in a deterministic, partial equilibrium framework. It is shown that the dividend and arbitrage approaches to valuation are not equivalent in general. A necessary and sufficient condition for their equivalence is also obtained.     

Credit risk model with contagious default dependencies affected by macro-economic condition

We consider a credit risk model with two industrial sectors, where defaults of corporations would be influenced by two factors. The first factor represents the macro economic condition which would affect the default intensities of the two industrial sectors differently. The second factor reflects the influences of the past defaults of corporations against other active corporations, where such influences would affect the two industrial sectors differently. A two-layer Markov chain model is developed, where the macro economic condition is described as a birth-death process, while another Markov chain represents the stochastic characteristics of defaults with default intensities dependent on the state of the birth-death process and the number of defaults in two sectors. Although the state space of the two-layer Markov chain is huge, the fundamental absorbing process with a reasonable state space size could capture the first passage time structure of the two-layer Markov chain, thereby enabling one to evaluate the joint probability of the number of defaults in two sectors via the uniformization procedure of Keilson. This in turn enables one to value a variety of derivatives defined on the underlying credit portfolios. In this paper, we focus on a financial product called CDO, and a related option.     

Minimizing loss probability bounds for portfolio selection

In this paper, we derive a portfolio optimization model by minimizing upper and lower bounds of loss probability. These bounds are obtained under a nonparametric assumption of underlying return distribution by modifying the so-called generalization error bounds for the support vector machine, which has been developed in the field of statistical learning. Based on the bounds, two fractional programs are derived for constructing portfolios, where the numerator of the ratio in the objective includes the value-at-risk (VaR) or conditional value-at-risk (CVaR) while the denominator is any norm of portfolio vector. Depending on the parameter values in the model, the derived formulations can result in a nonconvex constrained optimization, and an algorithm for dealing with such a case is proposed. Some computational experiments are conducted on real stock market data, demonstrating that the CVaR-based fractional programming model outperforms the empirical probability minimization.     

Optimal construction and rebalancing of index-tracking portfolios

Index funds aim to track the performance of a financial index, such as, e.g., the Standard?&?Poor’s?500 index. Index funds have become popular because they offer attractive risk-return profiles at low costs. The index-tracking problem considered in this paper consists of rebalancing the composition of the index fund’s tracking portfolio in response to new market information and cash deposits and withdrawals from investors such that the index fund’s tracking accuracy is maximized. In a frictionless market, maximum tracking accuracy is achieved by investing the index fund’s entire capital in a tracking portfolio that has the same normalized value development as the index. In the presence of transaction costs, which reduce the fund’s capital, one has to manage the trade-off between transaction costs and similarity in terms of normalized value developments. Existing mathematical programing formulations for the index-tracking problem do not optimize this trade-off explicitly, which may result in substantial transaction costs or tracking portfolios that differ considerably from the index in terms of normalized value development. In this paper, we present a mixed-integer linear programing formulation with a novel optimization criterion that directly considers the trade-off between transaction costs and similarity in terms of normalized value development. In an experiment based on a set of real-world problem instances, the proposed formulation achieves a considerably higher tracking accuracy than state-of-the-art formulations.     

Patterns in stock market movements tested as random number generators

This paper shows that tests of Random Number Generators (RNGs) may be used to test the Efficient Market Hypothesis (EMH). It uses the Overlapping Serial Test (OST), a standard test in RNG research, to detect anomalous patterns in the distribution of sequences of stock market movements up and down. Our results show that most stock markets exhibit idiosyncratic recurrent patterns, contrary to the efficient market hypothesis; also that OST detects a different kind of non-randomness to standard econometric long- and short-memory tests. Exposure of these anomalies should contribute to making markets more efficient.     

Does the financial market compensate investors for operational Losses?

It is well known that several industries, like the hotel industry, are subject to low frequency high impact events resulting from their operations. However, there is a dearth of academic research in this area. In this paper we propose an innovative methodology to study the problem using a combination of Asset Pricing Models and an original database. We find that asset prices compensate investors not only for market and credit risk, but also for operational risk.     

Trade credit for supply chain coordination

Trade-credit is a seller’s short-term loan to the buyer, allowing the buyer to delay payment of an invoice. It has been the largest source of working capital for a majority of business-to-business firms in the United States. Numerous theories have been proposed to explain trade-credit, mainly from finance perspectives. It has also been an important issue in supply chain management. Surprisingly, most literature in supply chain management has examined the retailer’s stocking policies given a supplier’s trade-credit. This paper attempts to shed light on trade-credit from a supplier’s perspective, and presents it as a tool for supply chain coordination. Specifically, we explicitly assume firms’ financial needs for inventory. Following a Newsvendor framework, we assume that the supplier grants trade-credit and markdown allowance. Given the supplier’s offer, the retailer determines order quantity and the financing option for the inventory, either trade-credit or direct financing from a financial institution. Our result shows that the supplier’s markdown allowance alone cannot fully coordinate the supply chain if the retailer employs direct financing. Positive financing costs call for trade-credit in order to subsidize the retailer’s costs of inventory financing. Using trade-credit in addition to markdown allowance, the supplier fully coordinates the retailer’s decisions for the largest joint profit, and extracts a greater portion of the maximized joint profit.     

Alternative optimality criteria of portfolio selection based upon threshold stopping rule

This paper proposes two types of alternative criteria of optimality for the continuous time portfolio selection problem. The optimality criteria, the so–called Laplace–Stieltjes transform (LST) criteria, are based on the assumption that the financial agent has a target level for the wealth accumulation process. These criteria are closely related to the so–called threshold stopping investment rule. We analytically derive the LST criteria and numerically compare them with the well–known Kelly criterion. It is shown that the portfolio strategies suggested may overcome the problem that the growth portfolio is often overestimated in several investment situations.