# Arbitrage and Geometry

@article{Naiman2017ArbitrageAG, title={Arbitrage and Geometry}, author={Daniel Q. Naiman and Edward R. Scheinerman}, journal={arXiv: Mathematical Finance}, year={2017} }

This article introduces the notion of arbitrage for a situation involving a collection of investments and a payoff matrix describing the return to an investor of each investment under each of a set of possible scenarios. We explain the Arbitrage Theorem, discuss its geometric meaning, and show its equivalence to Farkas' Lemma. We then ask a seemingly innocent question: given a random payoff matrix, what is the probability of an arbitrage opportunity? This question leads to some interesting…

## 2 Citations

### Farkas Certificates and Minimal Witnesses for Probabilistic Reachability Constraints

- Computer ScienceTACAS
- 2020

Farkas certificates for lower and upper bounds on minimal and maximal reachability probabilities in Markov decision processes (MDP) are introduced using an MDP-variant of Farkas’ Lemma.

### Tools and Algorithms for the Construction and Analysis of Systems: 26th International Conference, TACAS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25–30, 2020, Proceedings, Part II

- Computer ScienceTACAS
- 2020

This work implemented a standalone PDR algorithm and a PDR-based auxiliary-invariant generator for k -induction, and performed an experimental study on the largest publicly available benchmark set of C verification tasks, in which the effectiveness and efficiency of software verification with PDR are explored.

## References

SHOWING 1-10 OF 32 REFERENCES

### An elementary introduction to mathematical finance

- Economics
- 2002

This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance.…

### The Cost of Capital, Corporation Finance and the Theory of Investment

- Economics
- 1958

The potential advantages of the market-value approach have long been appreciated; yet analytical results have been meager. What appears to be keeping this line of development from achieving its…

### A Simple Approach to the Valuation of Risky Streams

- Economics
- 1978

The optimal investment decision or the capital budgeting problem in a competitive environment are equivalent to the problem of valuing a stream of returns. If the returns from a project can be…

### The Arbitrage Principle in Financial Economics

- Economics
- 1987

Abstract The importance of arbitrage conditions in financial economics has been recognized since Modigliani and Miller's classic work on the financial structure of the firm. They showed that if a f...

### Cost of capital.

- EconomicsHospital financial management
- 1978

The purpose of this section is to show you how the required rate of return for a firm (or for an individual for that matter) is determined and what the value for the required Rate of return means.

### The Pricing of Options and Corporate Liabilities

- EconomicsJournal of Political Economy
- 1973

If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this…

### Random polytopes: Their definition, generation and aggregate properties

- MathematicsMath. Program.
- 1982

It is shown that the expected number of extreme points for such random polytopes increases monotonically in the number of constraints to the limiting case of a polytope topologically equivalent to a hypercube.

### EXTREMAL ARRANGEMENTS OF HYPERPLANES a

- Mathematics
- 1985

An arrangement of hyperplanes is a finite set of hyperplanes in real projective or Euclidean (affine) space, regarded as dissecting the space into cells (or faces) of various dimensions. The Jiats of…