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22:
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Assume further that there is 50% transaction costs for each deal. This means that (1A,-1M) and (-1A,1M) cannot be exchanged into non-negative portfolios. But, (2A,-1M) and (-1A,2M) can be traded into non-negative portfolios. It can be seen that
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717:) are the set of prices which would define a friction-less pricing system for the assets that is consistent with the market. This is also called a
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Schachermayer, Walter (November 15, 2002). "The
Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time".
611:
The negative of a solvency cone is the set of portfolios that can be obtained starting from the zero portfolio. This is intimately related to
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The dual cone of prices is thus easiest to see in terms of prices of A in terms of M (and similarly done for price of M in terms of A):
58:
145:
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of portfolios that can be exchanged to portfolios of non-negative components (including paying of any transaction costs).
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is the number of assets which with any non-negative quantity of them can be "discarded" (traditionally
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757:, we can obviously make (1A,-1M) and (-1A,1M) into non-negative portfolios, therefore
710:{\displaystyle K^{+}=\left\{w\in \mathbb {R} ^{d}:\forall v\in K:0\leq w^{T}v\right\}}
1380:
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contains a line, then there is an exchange possible without transaction costs.
1358:
1327:
Löhne, Andreas; Rudloff, Birgit (2015). "On the dual of the solvency cone".
619:
1290:
Hamel, A. H.; Heyde, F. (2010). "Duality for Set-Valued
Measures of Risk".
1234:
1313:
934:{\displaystyle K=\{x\in \mathbb {R} ^{2}:(2,1)x\geq 0,(1,2)x\geq 0\}}
1233:, then there is no possible exchange, i.e. the market is completely
1126:{\displaystyle (1,0)\rightarrow (0,t)\rightarrow ({\frac {t}{2}},0)}
1016:{\displaystyle (0,t)\rightarrow (1,0)\rightarrow (0,{\frac {1}{2}})}
1341:
745:
Assume there are 2 assets, A and M with 1 to 1 exchange possible.
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is a model of a financial market. This is sometimes called a
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204:{\displaystyle \Pi =\left(\pi ^{ij}\right)_{1\leq i,j\leq d}}
824:{\displaystyle K=\{x\in \mathbb {R} ^{2}:(1,1)x\geq 0\}}
597:{\displaystyle \left\{K_{t}(\omega )\right\}_{t=0}^{T}}
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422:{\displaystyle \pi ^{ij}e^{i}-e^{j},1\leq i,j\leq d}
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may be too technical for most readers to understand
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83:. This is of particular interest to markets with
525:{\displaystyle K\supseteq \mathbb {R} _{+}^{d}}
307:is the convex cone spanned by the unit vectors
300:{\displaystyle K(\Pi )\subset \mathbb {R} ^{d}}
733:Sample solvency cone with no transaction costs
8:
928:
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741:Sample solvency cone with transaction costs
485:{\displaystyle K\subseteq \mathbb {R} ^{d}}
831:. Note that (1,1) is the "price vector."
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59:Learn how and when to remove this message
43:, without removing the technical details.
79:which models the possible trades in the
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1226:{\displaystyle K=\mathbb {R} _{+}^{d}}
1292:SIAM Journal on Financial Mathematics
540:A process of (random) solvency cones
41:make it understandable to non-experts
7:
457:is any closed convex cone such that
1049:{\displaystyle t<{\frac {1}{2}}}
345:{\displaystyle e^{i},1\leq i\leq m}
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1133:therefore there is arbitrage if
1023:therefore there is arbitrage if
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1329:Discrete Applied Mathematics
87:. Specifically, it is the
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1058:someone offers tM for 1A:
948:someone offers 1A for tM:
263:), then the solvency cone
1351:10.1016/j.dam.2015.01.030
719:consistent pricing system
613:self-financing portfolios
1387:Financial risk modeling
230:{\displaystyle m\leq d}
1271:Cite journal requires
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1152:{\displaystyle t>2}
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835:With transaction costs
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622:of the solvency cone (
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77:financial mathematics
75:is a concept used in
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115:{\displaystyle \Pi }
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1167:If a solvency cone
755:frictionless market
749:Frictionless market
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256:{\displaystyle m=d}
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95:Mathematical basis
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1180:{\displaystyle K}
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450:{\displaystyle K}
142:assets such that
135:{\displaystyle d}
85:transaction costs
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81:financial market
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37:help improve it
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101:bid-ask matrix
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73:solvency cone
63:
60:
52:
49:December 2013
42:
38:
32:
29:This article
27:
18:
17:
1332:
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1322:
1298:(1): 66–95.
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1264:cite journal
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436:
98:
72:
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55:
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30:
1335:: 176–185.
99:If given a
89:convex cone
1242:References
1163:Properties
433:Definition
1359:0166-218X
1342:1402.2221
1300:CiteSeerX
1099:→
1081:→
989:→
971:→
923:≥
896:≥
860:∈
813:≥
777:∈
687:≤
675:∈
669:∀
651:∈
620:dual cone
567:ω
503:⊇
468:⊆
414:≤
402:≤
383:−
361:π
337:≤
331:≤
283:⊂
277:Π
222:≤
194:≤
182:≤
162:π
150:Π
110:Π
1381:Category
1367:12427504
1235:illiquid
725:Examples
35:Please
1365:
1357:
1302:
1363:S2CID
1337:arXiv
753:In a
1355:ISSN
1277:help
1144:>
1034:<
618:The
536:Uses
492:and
211:and
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71:The
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
