updates to non-ergodic post

categories/economics/index.html

@@ -249,7 +249,7 @@ <h2 class="post-title">Ergodicity and Insurance</h2>
     &nbsp;|&nbsp;<i class="fas fa-clock"></i>&nbsp;2&nbsp;minutes
 
 
-    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;251&nbsp;words
+    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;306&nbsp;words
 
 
 
@@ -264,7 +264,7 @@ <h2 class="post-title">Ergodicity and Insurance</h2>
     <div class="post-entry">
 
         I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.
         <a href="https://www.codelooper.com/post/2023-07-19-ergodicity-and-insurance/" class="post-read-more">[Read More]</a>
 
     </div>

categories/economics/index.xml

@@ -13,7 +13,7 @@
 
       <guid>https://www.codelooper.com/post/2023-07-19-ergodicity-and-insurance/</guid>
       <description>I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.</description>
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.</description>
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index.html

@@ -255,7 +255,7 @@ <h2 class="post-title">Ergodicity and Insurance</h2>
     &nbsp;|&nbsp;<i class="fas fa-clock"></i>&nbsp;2&nbsp;minutes
 
 
-    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;251&nbsp;words
+    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;306&nbsp;words
 
 
 
@@ -270,7 +270,7 @@ <h2 class="post-title">Ergodicity and Insurance</h2>
     <div class="post-entry">
 
         I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.
         <a href="https://www.codelooper.com/post/2023-07-19-ergodicity-and-insurance/" class="post-read-more">[Read More]</a>
 
     </div>

index.xml

@@ -13,7 +13,7 @@
 
       <guid>https://www.codelooper.com/post/2023-07-19-ergodicity-and-insurance/</guid>
       <description>I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.</description>
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.</description>
     </item>
 
     <item>

post/2023-07-19-ergodicity-and-insurance/index.html

@@ -9,7 +9,7 @@
 
   <title>Ergodicity and Insurance - Teddy&#39;s online desktop</title>
   <meta name="description" content="I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.">
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.">
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-  "description" : "I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.\nIt really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.",
+  "description" : "I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.\nIt seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.",
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 <meta property="og:description" content="I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.">
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.">
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-It really should be titled financial transactions as an ergodicity …">
+It seems intuitive that an equal chance bet that would allow you to …">
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@@ -276,7 +276,7 @@ <h1>Ergodicity and Insurance</h1>
     &nbsp;|&nbsp;<i class="fas fa-clock"></i>&nbsp;2&nbsp;minutes
 
 
-    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;251&nbsp;words
+    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;306&nbsp;words
 
 
 
@@ -303,7 +303,9 @@ <h1>Ergodicity and Insurance</h1>
     <div class="col-lg-8 col-lg-offset-2 col-md-10 col-md-offset-1">
       <article role="main" class="blog-post">
         <p>I read this post on <a href="https://www.linkedin.com/feed/update/urn:li:activity:7085565022042472448?updateEntityUrn=urn%3Ali%3Afs_feedUpdate%3A%28V2%2Curn%3Ali%3Aactivity%3A7085565022042472448%29">LinkedIn</a> by Andreas Tsanakas that referenced a paper by Ole Peters titled <a href="https://tinyurl.com/yc65c2h3">Insurance as an Ergodicity Problem</a>.</p>
-<p>It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.</p>
+<p>It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.</p>
+<p>This motivates the idea that financial transactions are a solution to an ergodicity problem. A transaction in financial markets (buy insurance, etc) provides long-term value retention and growth without needing to appeal to economic concepts of concavity of utility functions and risk-aversion.</p>
+<p>It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.</p>
 <p>I made a spreadsheet to illustrate the main points in the paper (<a href="/post/2023-07-19-ergodicity-and-insurance/Ergodicity.xlsx">Ergodicity Excel Model</a> ) which plots four random multiplicative series and 4 of the same with savings and withdrawals that would be similar to paying a premium in good years and getting an indemnity in poor years. I also tested the <a href="https://en.wikipedia.org/wiki/Kelly_criterion">Kelly Criterion</a> which might be the optimal solution (betting an optimal proportion of the wealth in each time period). The model could be made more realistic but I think it illustrates the point that using expected values (arithmetic average) leads to the wrong conclusions in some cases where there are multiplicative impacts in a dynamic system and that some forms of exchanges is motivated by individual&rsquo;s long-term thinking where expected values over groups may not be a good model for how people behave.</p>
 <img src="images/ergodicity_series.png" alt="ergodicity_series" width="80%"/>
 <p>Some other relevant posts on the subject:</p>

post/index.html

@@ -268,7 +268,7 @@ <h2 class="post-title">Ergodicity and Insurance</h2>
     &nbsp;|&nbsp;<i class="fas fa-clock"></i>&nbsp;2&nbsp;minutes
 
 
-    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;251&nbsp;words
+    &nbsp;|&nbsp;<i class="fas fa-book"></i>&nbsp;306&nbsp;words
 
 
 
@@ -283,7 +283,7 @@ <h2 class="post-title">Ergodicity and Insurance</h2>
     <div class="post-entry">
 
         I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.
         <a href="https://www.codelooper.com/post/2023-07-19-ergodicity-and-insurance/" class="post-read-more">[Read More]</a>
 
     </div>

post/index.xml

@@ -13,7 +13,7 @@
 
       <guid>https://www.codelooper.com/post/2023-07-19-ergodicity-and-insurance/</guid>
       <description>I read this post on LinkedIn by Andreas Tsanakas that referenced a paper by Ole Peters titled Insurance as an Ergodicity Problem.
-It really should be titled financial transactions as an ergodicity problem: A way to model why people transact in financial markets (buy insurance, etc) without needing to appeal to concavity of utility functions and risk-aversion. It also explains how saving part of your income in each time period and investing only a fraction of your wealth in any gamble makes sense (a type of self-insurance) when the outcomes have multiplicative and not additive impacts on your life as it surely does in the real world.</description>
+It seems intuitive that an equal chance bet that would allow you to win 50% or lose 40% of the value of the bet would have a positive expected value, but in the long run such a bet will bankrupt you if you bet it all each time.</description>
     </item>
 
     <item>