A Bound on the Financial Value of Information

Abstract --It will be shown that each bit of information at most doubles the resulting wealth in the general stock market setup. This information bound on the growth of wealth is actually' attained for certain probability distributions on the market investigated by Kelly. The bound will be shown to be a special case of the result that the increase in exponential growth of wealth achieved with true knowledge of the stock market distribution F over that achieved with incorrect knowledge G is bounded above by D( FllG), the entropy of F relative to G

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

Optimal portfolio with insider information on the stochastic interest rate

We consider the optimal portfolio problem where the interest rate is stochastic and the agent has insider information on its value at a finite terminal time. The agent's objective is to optimize the terminal value of herportfolio under a logarithmic utility function. Using techniques of initial enlargement of filtration, we identify the optimal strategy and compute the value of the information. The interest rate is first assumed to be an affine diffusion, then more explicit formulas are computed for the Vasicek interest rate model where the interest rate moves according to an Ornstein-Uhlenbeck process. We show that when the interest rate process is correlated with the price process of the risky asset, the value of the information is infinite, as is usually the case for initial-enlargement-type problems. However, since the agent does not know exactly the correlation factor, this may induce an infinite loss instead of an infinite gain. Finally weakening the information own by the agent, and assuming that she only knows a lower-bound for the terminal value of the interest rate process, we show that the value of the information is finite.The first author acknowledge financial support from the Spanish Ministry of Education and Science, research projects MTM2015– 72907–EXP and MTM2013–42104–P (via FEDER funds)

Value of information in the binary case and confusion matrix

The simplest Bayesian system used to illustrate ideas of probability theory is a coin and a boolean utility function. To illustrate ideas of hypothesis testing, estimation or optimal control, one needs to use at least two coins and a confusion matrix accounting for the utilities of four possible outcomes. Here we use such a system to illustrate the main ideas of Stratonovich’s value of information (VoI) theory in the context of a financial time-series forecast. We demonstrate how VoI can provide a theoretical upper bound on the accuracy of the forecasts facilitating the analysis and optimization of models

Essays on Monetary Economics

My dissertation, which consists of three papers, is devoted to studying the implications of conventional and unconventional monetary policies for inflation, asset prices, and welfare. The first paper examines the sustainability and effectiveness of negative nominal interest rates. I construct a model of multiple means of payment where the cost of holding paper currency—its storage and security costs—determines the effective rate of return on currency, which establishes the effective lower bound on nominal interest rates. I show that central banks can reduce the effective rate of return on currency, and thus the effective lower bound, by altering their policy on bank reserves. However, reducing the lower bound leads to welfare losses associated with individuals holding more currency. Moreover, sustaining a negative rate by reducing the lower bound has no stimulative effects. This occurs because this policy combination reduces both the rate of return on currency and interest rates on financial assets, leaving the relative interest rates between currency and financial assets unchanged. In the second paper, I develop a two-country model with financial frictions to study how a central bank\u27s unconventional asset purchases affect international asset prices and welfare. In the model, the key financial frictions are limited commitment, differential pledgeability of assets as collateral, and a scarcity of collateralizable assets. Due to the differential pledgeability of assets, financial intermediaries acquire different asset portfolios depending on their home country. I find that quantitative easing can reduce long-term bond yields and term premia internationally and depreciate the creditor country\u27s currency. Foreign exchange intervention always depreciates the local currency, but it can improve welfare globally if implemented by the creditor country. The third paper studies the implications of heterogeneous payment choices for monetary policy. I construct a model of money and credit where each consumer participates in a small-value or a large-value transaction depending on a preference shock. Financial intermediaries write deposit contracts for consumers to intermediate credit transactions. The preference shock is private information and is costly for intermediaries to observe. I find that, in equilibrium, financial intermediaries create state-contingent deposit contracts for consumers. However, private information and costly monitoring generate an incentive problem, so that the quantity of credit is constrained for consumers in large-value transactions. The effects of monetary policy on the allocation of means of payment vary depending on the size of transaction

Determinants of Community Decisions To Lend Money To Loaners

Purpose: To meet the needs of the public, the government has provided an official financial institution, which is subject to a certain series of administrations with all the calculations. The problem is that not all community members understand access to finance at these financial institutions. There are Islamic banking, BMT, and Sharia KSPPS, but in borrowing money they choose moneylenders. This problem is influenced by the ease of borrowing money from moneylenders, which are more flexible and the method of payment can be adjusted according to a special agreement between the customer and the moneylender. Disbursement of funds that can be done at any time according to the time needed, without being bound by conditions that are considered complicated by the customer. As a form of compensation, the interest charged by moneylenders is high and burdensome for the borrower. The risk of high-interest rates is often not taken into account by the borrower.   Design/Methodology/Approach: The method for developing public financial literacy is what the moneylender's practice as the object of observation. To be realized as an effort for educational methods is to conduct an analysis of moneylenders in the community and explore how people depend on moneylenders, evaluate financial behavior in the community, deconstruct financial behavior and re-conceptualize public financial behavior.   Findings: Socialization and acceleration of the marketing of financial products from the BMT, or official government financial institutions need to be carried out to prevent the level of community dependence on moneylenders, including by expanding financial literacy in the community, establishing management education methods, and implementing finance that is more inclusive in the community.   Research, Practical & Social Implications: The necessities of life for each individual in the community will certainly not be the same, to be able to fulfill the purpose of these needs it is financed by the availability of funds or financial means. There are members of the community who are relatively able to meet their financing needs, but not a few of the community have not met their needs.   Originality/Value: This study seeks to help the government and society in Indonesia to have a good education in terms of financial literacy, people need information and knowledge that currently in Indonesia there are many formal and legal financial institutions to help financial problems faced by people in Indonesia. Indonesian people are no longer just dependent on moneylenders or illegal financial institutions, which will instead trap them into new financial problems

Security analysis of finance and healthcare android applications

Thesis (M.S.)--Boston UniversityAndroid is a major mobile operating system pre-installed and shipped with more than 60% of smart-phones in the market. The open source nature of android en- courages developers to innovate wide-range of applications. Meantime, the sweeping android acceptance with individuals and industries caught the attention of malicious software writers, which led to a sharp increase of security threats. Such threats raise a deeper concern in financial and healthcare applications that are inherently bound to handle private and sensitive information. The research provides a deeper analysis on security vulnerabilities of android applications in finance and healthcare category, from official Google app store. It is proposed and implemented a security analysis framework that takes account of a wide range of vulnerability metrics to provide unified and quantified method of measuring android applications vulnerability. The framework implementation automated the process of crawling google's app store, downloading applications package to a repository and conducting vulnerability analysis. It automatically extracts security parameters, measures vulnerability metrics and generates vulnerability report. The security parameters were extracted from manifest, de-compiled source code and app store meta-data. The analysis, on the top 632 free apps from finance and medical category revealed that on average financial apps found to be more vulnerable than medical apps. Medical apps have the maximum value for all types of vulnerabilities. Furthermore, a descriptive statistical analysis on the vulnerability metrics revealed that there is a linear relationship between implicitly open components and the number of times they access sensitive android resources

ASP -pricing: A Black -Scholes option pricing formulation

The Applications Service Provider (ASP) arrangement has engendered a revolution in the area of corporate information technology (IT) by transforming software from a packaged off-the-shelf product to an on-line virtual service. The focus of this study is to establish a sound mathematical foundation for evaluating software rental agreements (embedding exit flexibility) by incorporating a real options framework (based upon the Black-Scholes approach) into the traditional capital budgeting technique. The static discounted cash flow or net present value analysis may not adequately serve as a ‘barometer’ of outsourcing value due to its inherent weaknesses. On the other hand, the options approach to valuing real investments appropriately prices the state-contingent opportunity risk of outsourcing flexibility in the model\u27s variance parameter. ASP or outsourcing mechanisms embedding the exit (or, deferral) option are developed and examined from the viewpoint of the renter as well as the subcontractor. From the renter\u27s perspective, the value of the flexible outsourcing contract is modeled as a combination of tangible and intangible payoffs. A numerical illustration is used to demonstrate the applicability of the proposed model. The intangible payoff (given applications software alternatives), which is evaluated within the Margrabe\u27s simple exchange option model, is found to increase at higher volatility levels, with the highest option prices (and investment values) tending to occur where the technological divergence between underlying applications environments is the greatest. Therefore, while evaluating rental software alternatives, IT managers should also consider the underlying applications technology in terms of the directional impact of new information. From the subcontractor\u27s perspective, the value of the flexible outsourcing contract is modeled as a combination of a continuing ASP arrangement and the ‘aggregate’ option premium. A numerical analysis is conducted using actual data to examine model outcomes in the light of some results gleaned from related financial and real options literature. The value of exit flexibility, calculated as a ‘truncated’ nested call within a modified version of Carr\u27s compound exchange option model, is less than the commonly designated upper bound. The analysis also reveals that the intermediate exit options can be expressed in terms of the terminal exit opportunity. Hence, one may obtain the outsourcing value by easily ‘weighing’ the simple option premium for the final decision implementation point with the appropriate ‘probability-discount’ factor. Further, consecutive options in the nested series exhibit a decreasing price trend as is observed under other multi-stage options scenarios. Finally, the study develops a theory of optimal exit times for outsourcing contracts that are designed to continue indefinitely into the future. (Abstract shortened by UMI.

The Theory of Money

Fiat money(1) is a creation of both the state and society. Its value is supported by expectations which are conditioned by the dynamics of trust in government, the socio-economic structure and by outside events such as wars, plagues or political unrest. The micro-management of a dynamic economy is not far removed in difficulty from the micro-management of the weather. However, money and the financial institutions and instruments of a modern economy provide the means to influence expectations and bound behavior.(2) Paper money emerges as a virtual commodity. The dynamics of the economy permits it to serve as an imaginary gold.Although it is an abstraction, it is meaningful to talk about its quantity. Closely related to but basically different from fiat money is credit.(3) Credit, unlike fiat money is not a virtual commodity but a two party contract. The fact that it is a two party contract set in a dynamic context implies that there are chances that the economy may reach a state where a debtor is unable to meet his or her obligations. When this happens the laws and customs of the society must provide default, bankruptcy and reorganization rules. These rules are usually denominated in terms of fiat and socio-economic penalties such as the confiscation of assets, garnishing of salary or time in debtors' prison. Thus the value of paper gold is determined in two ways by the dynamics of the system. First by acceptance in trade, based on the expectation that it will remain valuable and second by its role in the discharge of debts where failure to repay has unpleasant consequences. When taxes are present a third valuation appears in the penalties for failure to pay taxes. The control of the fiat money supply together with rules on the granting of credit and the bankruptcy, default and reorganization rules,in essence, provide lower and upper bounds for the price level in the economy. They also determine the innovation rate of the economy. An innovation may be regarded as an economic mutation; the less costly failure is, the more likely an innovation will be risked. The rates of interest for loans combined with the harshness of the bankruptcy and reorganization laws help to determine the rate of innovation in a society. Government controls only one among many interest rates. A host of institutional details involving risk and transactions cost determine the others. The velocity of both money and credit may vary. Even though velocity may vary, human decision-making takes a finite amount of time. This implies that velocity will remain bounded. Beyond some speed of circulation expectations will degenerate and the economy will break down. In order to appreciate the intrinsic dynamics of a high information and communication mass economy at least three agents must be distinguished. They are the highly visible government; other largely visible legal persons, such as banks and corporations and real persons. Their differences are characterized by their relative power and the size of their communication networks. The contrast between a market economy and a state economy is not a clean contrast. The distinctions are on a continuum. Among modern democratic market economies the size of the government sector is roughly anywhere from 15% to 50% of the economy. Thus the control description of virtually any modern economy is of one extremely large and visible player; at most a few hundred large corporate entities of reasonably high visibility and a mass of small agents known by and in direct communication with only a few others. The reconciliation of a dynamics oriented macro-economics with an equilibrium oriented micro-economics lies in the understanding that the economy is embedded in the polity and society. The institutions, customs and laws are the carriers of process and provide bounds to process. They limit the dynamics.The role of macroeconomic policy is to bound the dynamics of an evolving society. Individual behavior is local and necessarily myopic. Myopic local optimization is consistent with global evolution. An elementary understanding of history and the decision and game theory proliferation of strategies is enough to indicate that the search for a unique or even stationary economic dynamics is an essay in futility.In contrast the search for the correct carriers and bounds on process is feasible.The monetary structure provides the sufficient loose coupling to permit mass independent behavior to take place even somewhat chaotically within institutional bounds.(4) 1. I use the term fiat or abstract paper money interchangeably to stand for a government supplied means of payment of no intrinsic worth. 2. Phrasing this somewhat more technically they provide the bounds on the state space. A state space is the set of all feasible states which can be achieved by the system. 3. Credit such as bank credit from a well known bank may be referred to as "inside money" in the sense that it is a contract between two legal persons in the economy other than the government. Yet the bank credit, because of the visibility and reputation of the bank, may serve as a substitute in transactions for fiat money. 4. Technically the institutions and the monetary and financial structure fully define the state space, but do not describe the dynamics. There is a robust collection of local individual rules of behavior which are all sufficient to provide the dynamic support of expectations that money will be accepted as having value. The control system may be sufficient to guide or at least limit the overall macroeconomic behavior without necessarily providing for a precise or unique dynamics. Money is the only financial instrument without an offsetting instrument. This nonsymmetry appears to be critical in the introduction of time into the model of the economy.Money, macro-economics, strategic market games, general disequilibrium, bankruptcy