Bi-directional grid absorption barrier constrained stochastic processes with applications in finance & investment

Whilst the gambler’s ruin problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required for the grid trading problem (GTP) of financial markets, especially foreign exchange (FX) markets. As banks and financial institutions have the requirement to hedge their FX exposure, the GTP can help provide a framework for greater automation of the hedging process and help forecast which hedge scenarios to avoid. Two theorems are adapted from GRP to GTP and prove that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. We introduce two absorption barriers, one at zero balance (ruin) and one at a specified profit target. This extends the traditional GRP and the GTP further by deriving both the probability of ruin and the expected number of steps (of reaching a barrier) to better demonstrate that GTP takes longer to reach ruin than GRP. These statistical results have applications into finance such as multivariate dynamic hedging (Noorian, Flower, & Leong, 2016), portfolio risk optimization, and algorithmic loss recovery.

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Gambler’s ruin problem and bi-directional grid constrained trading and investment strategies

Investment Management and Financial Innovations ◽

10.21511/imfi.17(3).2020.05 ◽

2020 ◽

Vol 17 (3) ◽

pp. 54-66 ◽

Cited By ~ 1

Author(s):

Aldo Taranto ◽

Shahjahan Khan

Keyword(s):

Financial Markets ◽

Research Training ◽

Investment Strategies ◽

Short Term ◽

Investment Funds ◽

Innovation Potential ◽

Research Training Program ◽

Gambler’S Ruin ◽

Gambler's Ruin Problem ◽

Ruin Problem

Bi-Directional Grid Constrained (BGC) trading strategies have never been studied academically until now, are relatively new in the world of financial markets and have the ability to out-perform many other trading algorithms in the short term but will almost surely ruin an investment account in the long term. Whilst the Gambler’s Ruin Problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required to solve the grid trading problem (GTP), i.e. a form of BGC financial markets strategies, and how it can deliver greater return on investment (ROI) for the same level of risk. A novel theorem of GTP is derived, proving that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. These results not only can be studied within mathematics and statistics in their own right, but also have applications into finance such as multivariate dynamic hedging, investment funds, trading, portfolio risk optimization and algorithmic loss recovery. In today’s uncertain and volatile times, investment returns are between 2%-5% per annum, barely keeping up with inflation, putting people’s retirement at risk. BGC and GTP are thus a rich source of innovation potential for improved trading and investing. Acknowledgement(s)Aldo Taranto was supported by an Australian Government Research Training Program (RTP) Scholarship. The authors would like to thank A/Prof. Ravinesh C. Deo and A/Prof. Ron Addie of the University of Southern Queensland for their invaluable advice on refining this paper.

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n-point, win-by-k games

Journal of Applied Probability ◽

10.2307/3214385 ◽

1989 ◽

Vol 26 (4) ◽

pp. 807-814 ◽

Cited By ~ 7

Author(s):

Kyle Siegrist

Keyword(s):

Exit Time ◽

Bernoulli Trials ◽

Expected Number ◽

First Exit Time ◽

World Series ◽

Time Space ◽

Gambler’S Ruin ◽

Gambler's Ruin Problem ◽

Positive Integers ◽

Made In

Consider a sequence of Bernoulli trials between players A and B in which player A wins each trial with probability p∈ [0, 1]. For positive integers n and k with k ≦ n, an (n, k) contest is one in which the first player to win at least n trials and to be ahead of his opponent by at least k trials wins the contest. The (n, 1) contest is the Banach match problem and the (n, n) contest is the gambler's ruin problem. Many real contests (such as the World Series in baseball and the tennis game) have an (n, 1) or an (n, 2) format. The (n, k) contest is formulated in terms of the first-exit time of the graph of a random walk from a certain region of the state-time space. Explicit results are obtained for the probability that player A wins an (n, k) contest and the expected number of trials in an (n, k) contest. Comparisons of (n, k) contests are made in terms of the probability that the stronger player wins and the expected number of trials.

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n-point, win-by-k games

Journal of Applied Probability ◽

10.1017/s0021900200027674 ◽

1989 ◽

Vol 26 (04) ◽

pp. 807-814 ◽

Cited By ~ 3

Author(s):

Kyle Siegrist

Keyword(s):

Exit Time ◽

Bernoulli Trials ◽

Expected Number ◽

First Exit Time ◽

World Series ◽

Time Space ◽

Gambler’S Ruin ◽

Gambler's Ruin Problem ◽

Positive Integers ◽

Made In

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Perspectives on inflation Targeting Regime in Russia

Voprosy Ekonomiki ◽

10.32609/0042-8736-2014-11-107-121 ◽

2014 ◽

pp. 107-121 ◽

Cited By ~ 1

Author(s):

S. Andryushin

Keyword(s):

Monetary Policy ◽

Financial Markets ◽

Interest Rates ◽

Inflation Targeting ◽

Short Term ◽

Indirect Control ◽

Financial Account ◽

Domestic Prices ◽

Macroeconomic Indicators ◽

Private And Public

The paper analyzes monetary policy of the Bank of Russia from 2008 to 2014. It presents the dynamics of macroeconomic indicators testifying to inability of the Bank of Russia to transit to inflation targeting regime. It is shown that the presence of short-term interest rates in the top borders of the percentage corridor does not allow to consider the key rate as a basic tool of monetary policy. The article justifies that stability of domestic prices is impossible with-out exchange rate stability. It is proved that to decrease excessive volatility on national consumer and financial markets it is reasonable to apply a policy of managing financial account, actively using for this purpose direct and indirect control tools for the cross-border flows of the private and public capital.

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Impact of FII’s and FDI’s on Indian Stock Market

Adhyayan A Journal of Management Sciences ◽

10.21567/adhyayan.v1i1.10220 ◽

2016 ◽

Vol 1 (1) ◽

Author(s):

Dr. Kamlesh Kumar Shukla

Keyword(s):

Stock Market ◽

Financial Markets ◽

Global Economy ◽

Short Term ◽

Earnings Growth ◽

The Past ◽

Bull Market ◽

Indian Stock Market

FIIs are companies registered outside India. In the past four years there has been more than $41 trillion worth of FII funds invested in India. This has been one of the major reasons on the bull market witnessing unprecedented growth with the BSE Sensex rising 221% in absolute terms in this span. The present downfall of the market too is influenced as these FIIs are taking out some of their invested money. Though there is a lot of value in this market and fundamentally there is a lot of upside in it. For long-term value investors, there’s little because for worry but short term traders are adversely getting affected by the role of FIIs are playing at the present. Investors should not panic and should remain invested in sectors where underlying earnings growth has little to do with financial markets or global economy.

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A Note Concerning the Dynamics of Government Bond Yields

The American Economist ◽

10.1177/0569434520988275 ◽

2021 ◽

pp. 056943452098827

Author(s):

Tanweer Akram

Keyword(s):

Interest Rate ◽

Financial Markets ◽

Yield Curve ◽

Empirical Studies ◽

State Theory ◽

Government Bond ◽

Bond Yields ◽

Short Term ◽

Government Bonds

Keynes argued that the central bank can influence the long-term interest rate on government bonds and the shape of the yield curve mainly through the short-term interest rate. Several recent empirical studies that examine the dynamics of government bond yields not only substantiate Keynes’s view that the long-term interest rate responds markedly to the short-term interest rate but also have relevance for macroeconomic theory and policy. This article relates Keynes’s discussions of money, the state theory of money, financial markets, investors’ expectations, uncertainty, and liquidity preference to the dynamics of government bond yields for countries with monetary sovereignty. Investors’ psychology, herding behavior in financial markets, and uncertainty about the future reinforce the effects of the short-term interest rate and the central bank’s monetary policy actions on the long-term interest rate. JEL classifications: E12; E40; E43; E50; E58; E60; F30; G10; G12; H62; H63

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Measuring the Short-Term Effects of the ECB’s Unconventional Monetary Policy on Financial Markets: A Review

Credit and Capital Markets – Kredit und Kapital ◽

10.3790/ccm.54.1.37 ◽

2021 ◽

Vol 54 (1) ◽

pp. 37-77

Author(s):

Lisa-Maria Kampl

Keyword(s):

Monetary Policy ◽

Financial Markets ◽

Event Studies ◽

Empirical Literature ◽

Unconventional Monetary Policy ◽

Short Term ◽

Comprehensive Overview ◽

Announcement Effects ◽

Policy Measures ◽

Short Term Effects

Following the financial crisis in 2008, the ECB implemented various unconventional policy measures to respond to the tensions on the market. These measures had a significant impact and short-term effects on financial markets. This literature review provides a extensive overview of the empirical literature dealing with the short-term effects of this unconventional monetary policy using event studies. Furthermore, a methodological analysis of conducted event studies is carried out. First, we review empirical event studies focusing on the effects on the bond market, the stock market, as well as on international spill-over effects. Secondly, we carry out a methodological analysis of event studies that estimate the announcement effects of the ECB’s unconventional measures. In this context, the analysis provides insight into the process of determining relevant events, the categorization of those, measuring the surprise component, and determining control variables. By comparing the different approaches applied, we give a comprehensive overview of similarities as well as differences in the methodology used.

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On a non-homogeneous difference equation from probability theory

Tatra Mountains Mathematical Publications ◽

10.2478/v10127-009-0027-4 ◽

2009 ◽

Vol 43 (1) ◽

pp. 81-90 ◽

Cited By ~ 1

Author(s):

Jean-Luc Guilbault ◽

Mario Lefebvre

Keyword(s):

Probability Theory ◽

Markov Chain ◽

Difference Equation ◽

Mathematical Expectation ◽

Transition Probabilities ◽

Current State ◽

Constant Coefficients ◽

Gambler’S Ruin ◽

Gambler's Ruin Problem ◽

Ruin Problem

Abstract The so-called gambler’s ruin problem in probability theory is considered for a Markov chain having transition probabilities depending on the current state. This problem leads to a non-homogeneous difference equation with non-constant coefficients for the expected duration of the game. This mathematical expectation is computed explicitly.

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