scholarly journals No-arbitrage concepts in topological vector lattices

Positivity ◽  
2021 ◽  
Author(s):  
Eckhard Platen ◽  
Stefan Tappe
Keyword(s):  
Asset Pricing ◽  
Financial Market ◽  
General Framework ◽  
General Setting ◽  
Structural Condition ◽  
Trading Strategies ◽  
Banach Function Spaces ◽  
No Arbitrage ◽  
Vector Lattices ◽  
Initial Wealth

AbstractWe provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA$$_1$$ 1 and NA$$_1$$ 1 may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.

scholarly journals GOOD DEAL BOUNDS WITH CONVEX CONSTRAINTS

2017 ◽  
Vol 20 (02) ◽  
pp. 1750011
Author(s):  
TAKUJI ARAI
Keyword(s):  
Asset Pricing ◽  
Financial Market ◽  
Risk Measure ◽  
Good Deal ◽  
Upper And Lower Bounds ◽  
Convex Constraints ◽  
Market Models ◽  
Convex Risk Measure ◽  
No Arbitrage ◽  
Constrained Markets

We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai & Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk measure a good deal valuation; and study its properties. We also discuss superhedging cost and Fundamental Theorem of Asset Pricing for convex constrained markets.

scholarly journals On the existence of sure profits via flash strategies

2019 ◽  
Vol 56 (2) ◽  
pp. 384-397 ◽  
Author(s):  
Claudio Fontana ◽  
Markus Pelger ◽  
Eckhard Platen
Keyword(s):  
General Theory ◽  
Transaction Costs ◽  
Financial Market ◽  
High Frequency ◽  
Asset Prices ◽  
General Setting ◽  
Trading Strategies ◽  
Frequency Limit ◽  
Price Process ◽  
High Frequency Limit

AbstractWe introduce and study the notion of sure profits via flash strategies, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there are no sure profits via flash strategies if and only if asset prices do not exhibit predictable jumps. This result relies on the general theory of processes and provides the most general formulation of the well-known fact that, in an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable direction or magnitude at predictable times. We furthermore show that any price process is always right-continuous in the absence of sure profits. Our results are robust under small transaction costs and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.

scholarly journals On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang-Bang No-Arbitrage Criteria

2004 ◽  
Vol 14 (2) ◽  
pp. 201-221 ◽  
Author(s):  
Igor V. Evstigneev ◽  
Klaus Schurger ◽  
Michael I. Taksar
Keyword(s):  
Asset Pricing ◽  
Fundamental Theorem ◽  
No Arbitrage

scholarly journals Dating Capital Market Integration In The EMU

2011 ◽  
Vol 10 (3) ◽  
pp. 63
Author(s):  
Sergiy Rakhmayil
Keyword(s):  
Asset Pricing ◽  
Financial Market ◽  
Capital Market ◽  
Market Integration ◽  
Structural Breaks ◽  
Capital Market Integration ◽  
Market Variables

This paper analyzes the effect of the Euro on structural breaks in financial market variables in a sample of three EMU (France, Germany, Netherlands) and two non-EMU (U.K. and Switzerland) countries from March 1984 to November 2002. We identify two dates when integration-related structural breaks occurred in European asset pricing; the first in 1986 affected all sample countries whereas the second in 2000 affected only the EMU countries and could be attributed to the adoption of Euro in 1999.

scholarly journals A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 60
Author(s):  
Stanislaus Maier-Paape ◽  
Andreas Platen ◽  
Qiji Jim Zhu
Keyword(s):  
General Framework ◽  
Optimization Problem ◽  
Risk Measure ◽  
Efficient Frontier ◽  
Portfolio Theory ◽  
Trading Strategies ◽  
Performance Criteria ◽  
Market Model ◽  
Constant Weight ◽  
New Approach

This is Part III of a series of papers which focus on a general framework for portfolio theory. Here, we extend a general framework for portfolio theory in a one-period financial market as introduced in Part I [Maier-Paape and Zhu, Risks 2018, 6(2), 53] to multi-period markets. This extension is reasonable for applications. More importantly, we take a new approach, the “modular portfolio theory”, which is built from the interaction among four related modules: (a) multi period market model; (b) trading strategies; (c) risk and utility functions (performance criteria); and (d) the optimization problem (efficient frontier and efficient portfolio). An important concept that allows dealing with the more general framework discussed here is a trading strategy generating function. This concept limits the discussion to a special class of manageable trading strategies, which is still wide enough to cover many frequently used trading strategies, for instance “constant weight” (fixed fraction). As application, we discuss the utility function of compounded return and the risk measure of relative log drawdowns.

Analyzing the Influences of Passive Investment Strategies on Financial Markets via Agent-Based Modeling

2008 ◽  
pp. 224-238 ◽  
Author(s):  
Hiroshi Takahashi ◽  
Satoru Takahashi ◽  
Takao Terano
Keyword(s):  
Asset Pricing ◽  
Financial Markets ◽  
Financial Market ◽  
Investment Strategy ◽  
Agent Based Modeling ◽  
Investment Strategies ◽  
Agent Based Model ◽  
Efficient Market ◽  
Agent Based ◽  
Price Fluctuations

This chapter develops an agent-based model to analyze microscopic and macroscopic links between investor behaviors and price fluctuations in a financial market. This analysis focuses on the effects of Passive Investment Strategy in a financial market. From the extensive analyses, we have found that (1) Passive Investment Strategy is valid in a realistic efficient market, however, it could have bad influences such as instability of market and inadequate asset pricing deviations, and (2) under certain assumptions, Passive Investment Strategy and Active Investment Strategy could coexist in a Financial Market.

scholarly journals Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non-Gaussian OU Processes

2015 ◽  
Vol 2015 ◽  
pp. 1-20
Author(s):  
Wanyang Dai
Keyword(s):  
Risk Factors ◽  
Financial Market ◽  
Contingent Claim ◽  
Global Risk ◽  
Hedging Strategy ◽  
Put Options ◽  
No Arbitrage ◽  
Special Cases ◽  
External Risk ◽  
Non Gaussian

We prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semiexplicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck (NGOU) processes. Analytical and numerical examples are both presented to illustrate the effectiveness of our optimal strategy. Our study establishes the connection between our financial system and existing general semimartingale based discussions by justifying required conditions. More precisely, there are three steps involved. First, we firmly prove the no-arbitrage condition to be true for our financial market, which is used as an assumption in existing discussions. In doing so, we explicitly construct the square-integrable density process of the variance-optimal martingale measure (VOMM). Second, we derive a backward stochastic differential equation (BSDE) with jumps for the mean-value process of a given contingent claim. The unique existence of adapted strong solution to the BSDE is proved under suitable terminal conditions including both European call and put options as special cases. Third, by combining the solution of the BSDE and the VOMM, we reach the justification of the global risk optimality for our hedging strategy.

Asset Pricing Models and Financial Market Anomalies

2006 ◽  
Vol 19 (3) ◽  
pp. 1001-1040 ◽  
Author(s):  
Doron Avramov ◽  
Tarun Chordia
Keyword(s):  
Asset Pricing ◽  
Financial Market ◽  
Pricing Models ◽  
Market Anomalies ◽  
Asset Pricing Models
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