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

2020 ◽  
Vol 17 (3) ◽  
pp. 54-66 ◽  
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.

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

2020 ◽  
Vol 10 (3) ◽  
pp. 20-33
Author(s):  
Aldo Taranto ◽  
Shahjahan Khan
Keyword(s):  
Financial Markets ◽  
Distributional Analysis ◽  
Portfolio Risk ◽  
Expected Number ◽  
Short Term ◽  
Probability Of Ruin ◽  
Loss Recovery ◽  
Risk Optimization ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem

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.

scholarly journals On a non-homogeneous difference equation from probability theory

2009 ◽  
Vol 43 (1) ◽  
pp. 81-90 ◽  
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.

Gambler’s ruin problem on Erdős–Rényi graphs

2017 ◽  
Vol 468 ◽  
pp. 147-157
Author(s):  
Zoltán Néda ◽  
Larissa Davidova ◽  
Szeréna Újvári ◽  
Gabriel Istrate
Keyword(s):  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Ruin Problem

THE GAMBLER'S RUIN PROBLEM WITH CORRELATION

Biometrika ◽  
1955 ◽  
Vol 42 (3-4) ◽  
pp. 486-493 ◽  
Author(s):  
C. MOHAN
Keyword(s):  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Ruin Problem

A Gambler’s Ruin Problem

SIAM Review ◽  
1971 ◽  
Vol 13 (4) ◽  
pp. 569-570
Author(s):  
Michael L. Trombetta
Keyword(s):  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Ruin Problem

An Elementary Derivation of the Duration of Play in the Gambler’s Ruin Problem

2021 ◽  
Vol 52 (4) ◽  
pp. 299-301
Author(s):  
Greg Orosi ◽  
Ricardo Alfaro ◽  
Lixing Han ◽  
Kenneth Schilling
Keyword(s):  
Elementary Derivation ◽  
Gambler’S Ruin ◽  
Gambler's Ruin Problem ◽  
Ruin Problem

scholarly journals The Efficiency of Active Asset Allocation Funds in the Period of Instability at Financial Markets

2012 ◽  
Vol 12 (2) ◽  
pp. 147-159
Author(s):  
Wojciech Krawiec
Keyword(s):  
Financial Markets ◽  
Asset Allocation ◽  
Stock Exchange ◽  
Investment Strategies ◽  
Investment Portfolio ◽  
Investment Funds ◽  
Financial Reports ◽  
Return Rates ◽  
Adequate Information ◽  
Online Investing

Abstract The objective of the hereby paper is the assessment of domestic active asset allocation funds efficiency in the period of 2007-2012, including the comparison of earned return rates against the return rates obtained by other mixed funds, as well as WIG and WIG20 stock exchange indices. Additionally, the purpose of the paper is to analyse the investment policy applied by the above listed funds, carried out based on records included in adequate information prospectuses, and also having considered the investment portfolio compositions presented in annual and 6-month financial reports covering these funds. The assessment of applied investment strategies efficiency is performed based on 12-, 24-, 36-, 48- and 60- month return rates set at the end of 6-month reporting periods. The analysis covered only domestic open-end active asset allocation investment funds included in this group following the definition accepted by Analizy Online investing assets in financial instruments issued by entities, officially seated in Poland or outside Poland and valuating participation units in PLN, which have been operating for at least 24 months from the day of 30th June 2012.

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